Diffraction gratings formed by metasurfaces having differently oriented nanobeams

ABSTRACT

Metasurfaces provide compact optical elements in head-mounted display systems to, e.g., incouple light into or outcouple light out of a waveguide. The metasurfaces may be formed by a plurality of repeating unit cells, each unit cell comprising two sets or more of nanobeams elongated in crossing directions: one or more first nanobeams elongated in a first direction and a plurality of second nanobeams elongated in a second direction. As seen in a top-down view, the first direction may be along a y-axis, and the second direction may be along an x-axis. The unit cells may have a periodicity in the range of 10 nm to 1 μm, including 10 nm to 500 nm or 300 nm to 500 nm. Advantageously, the metasurfaces provide diffraction of light with high diffraction angles and high diffraction efficiencies over a broad range of incident angles and for incident light with circular polarization.

PRIORITY CLAIM

This application is a continuation of U.S. patent application Ser. No.15/880,404 filed on Jan. 25, 2018, which claims the benefit of priorityunder 35 U.S.C. § 119(e) of U.S. Provisional Application No. 62/451,608filed on Jan. 27, 2017 and U.S. Provisional Application No. 62/451,615filed on Jan. 27, 2017. The entire disclosure of each of these prioritydocuments is incorporated herein by reference.

INCORPORATION BY REFERENCE

This application incorporates by reference the entirety of each of thefollowing patent applications: U.S. application Ser. No. 14/331,218;U.S. application Ser. No. 14/641,376; U.S. Provisional Application No.62/012,273; U.S. Provisional Application No. 62/005,807; U.S.Provisional Application No. 62/333,067; and U.S. patent application Ser.No. 15/342,033.

BACKGROUND Field

The present disclosure relates to display systems and, moreparticularly, to augmented reality display systems.

Description of the Related Art

Modern computing and display technologies have facilitated thedevelopment of systems for so called “virtual reality” or “augmentedreality” experiences, in which digitally reproduced images or portionsthereof are presented to a user in a manner wherein they seem to be, ormay be perceived as, real. A virtual reality, or “VR”, scenariotypically involves the presentation of digital or virtual imageinformation without transparency to other actual real-world visualinput; an augmented reality, or “AR”, scenario typically involvespresentation of digital or virtual image information as an augmentationto visualization of the actual world around the user. A mixed reality,or “MR”, scenario is a type of AR scenario and typically involvesvirtual objects that are integrated into, and responsive to, the naturalworld. For example, an MR scenario may include AR image content thatappears to be blocked by or is otherwise perceived to interact withobjects in the real world.

Referring to FIG. 1, an augmented reality scene 1 is depicted. The userof an AR technology sees a real-world park-like setting 20 featuringpeople, trees, buildings in the background, and a concrete platform 30.The user also perceives that he “sees” “virtual content” such as a robotstatue 40 standing upon the real-world platform 1120, and a flyingcartoon-like avatar character 50 which seems to be a personification ofa bumble bee. These elements 50, 40 are “virtual” in that they do notexist in the real world. Because the human visual perception system iscomplex, it is challenging to produce AR technology that facilitates acomfortable, natural-feeling, rich presentation of virtual imageelements amongst other virtual or real-world imagery elements.

Systems and methods disclosed herein address various challenges relatedto AR and VR technology.

SUMMARY

According to some embodiments, an optical system includes a metasurfaceconfigured to diffract visible light having a wavelength. Themetasurface includes a plurality of repeating unit cells, where eachunit cell consists of two to four sets of nanobeams. A first set ofnanobeams are formed by one or more first nanobeams and a second set ofnanobeams are formed by a plurality of second nanobeams disposedadjacent to the one or more first nanobeams and separated from eachother by a sub-wavelength spacing. The one or more first nanobeams andthe plurality of second nanobeams are elongated in different orientationdirections. The unit cells repeat at a period less than or equal toabout 10 nm to 1 μm.

According to some other embodiments, an optical system includes awaveguide configured to propagate visible light, where the wave guideincludes a substrate having thereon a metasurface of the optical systemdescribed above, wherein the one or more first nanobeams and the secondnanobeams are arranged to diffract light at a diffraction angle relativeto the direction of an incident light, and to cause the diffracted lightto propagate in the substrate under total internal reflection.

According to some embodiments, a head-mounted display device isconfigured to project light to an eye of a user to display augmentedreality image content, where the head-mounted display device includes aframe configured to be supported on a head of the user. The displaydevice additionally includes a display disposed on the frame. At least aportion of the display includes one or more waveguides, where the one ormore waveguides are transparent and disposed at a location in front ofthe user's eye when the user wears the head-mounted display device, suchthat the transparent portion transmits light from a portion of anenvironment in front of the user to the user's eye to provide a view ofthe portion of the environment in front of the user. The display deviceadditionally includes one or more light sources. The display devicefurther includes at least one diffraction grating configured to couplelight from the light sources into the one or more waveguides or tocouple light out of the one or more waveguides, where the diffractiongrating includes a metasurface of the optical system described above.

According to yet other embodiments, a method of fabricating an opticalsystem comprises providing a substrate and forming on the substrate ametasurface comprising a plurality of unit cells. Forming themetasurface includes forming the unit cells consisting of two to foursets of nanobeams. Forming the unit cells includes forming a first setof nanobeams including one or more first nanobeams and forming a secondset of nanobeams adjacent to the one or more first nanobeams. Formingthe second set of nanobeams includes forming a plurality of secondnanobeams that are separated from each other by a sub-wavelengthspacing. The one or more first nanobeams and the plurality of secondnanobeams are elongated in different orientation directions. The unitcells repeat at a period less than or equal to about 10 nm to 1 μm.

According to some embodiments, an optical system includes a metasurfaceconfigured to diffract visible light having a wavelength, where themetasurface includes a plurality of repeating unit cells. Each unit cellincludes a first set of nanobeams, where two or more of the firstnanobeams have different widths. Each unit cell additionally includes asecond set of nanobeams, where two or more of the second nanobeams havedifferent widths. The second nanobeams are disposed adjacent to thefirst nanobeams and separated from each other by a sub-wavelengthspacing. Furthermore, the first nanobeams and the second nanobeams ofthe unit cells have different orientations.

According to other embodiments, a head-mounted display device isconfigured to project light to an eye of a user to display augmentedreality image content, where the head-mounted display device includes aframe configured to be supported on a head of the user. The displaydevice additionally includes a display disposed on the frame. At least aportion of the display includes one or more waveguides, where the one ormore waveguides are transparent and are disposed at a location in frontof the user's eye when the user wears the head-mounted display device,such that the transparent portion transmits light to the user's eye toprovide a view of the portion of the environment in front of the user.The display device additionally includes one or more light sources. Thedisplay device further includes at least one diffraction gratingconfigured to couple light from the light sources into the one or morewaveguides or to couple light out of the one or more waveguides, wherethe diffraction grating comprising a metasurface according to theoptical system described above.

According to yet other embodiments, a method of fabricating ametasurface, includes providing a substrate. The method additionallyincludes forming on the substrate a metasurface having a plurality ofunit cells. Forming the metasurface includes forming a first set ofnanobeams comprising two or more first nanobeams having differentwidths. Forming the metasurface additionally includes forming a secondset of nanobeams comprising two or more second nanobeams havingdifferent widths, where the second nanobeams are disposed adjacent tothe first nanobeams and are separated from each other by asub-wavelength spacing. The first nanobeams and the second nanobeamshave different orientations.

Examples of various other embodiments are provided below:

1. An optical system comprising:

-   -   a metasurface configured to diffract visible light having a        wavelength, the metasurface comprising:        -   a plurality of repeating unit cells, each unit cell            consisting of two to four sets of nanobeams, wherein:            -   a first set of nanobeams are formed by one or more first                nanobeams; and            -   a second set of nanobeams are formed by a plurality of                second nanobeams disposed adjacent to the one or more                first nanobeams and separated from each other by a                sub-wavelength spacing,            -   wherein the one or more first nanobeams and the                plurality of second nanobeams are elongated in different                orientation directions, and            -   wherein the unit cells repeat at a period less than or                equal to about 10 nm to 1 μm.

2. The optical system of Embodiment 1, wherein the one or more firstnanobeams and the second nanobeams are oriented at an angle relative toeach other to cause a phase difference between the visible lightdiffracted by the one or more first nanobeams and the visible lightdiffracted by the second nanobeams.

3. The optical system of Embodiment 2, wherein the phase difference istwice the angle.

4. The optical system of any of Embodiments 1-3, wherein the wavelengthin the visible spectrum corresponds to a blue light, a green light or ared light.

5. The optical system of any of Embodiments 1-4, wherein the one or morefirst nanobeams and the second nanobeams are oriented in orientationdirections that are rotated by about 90 degrees relative to each other.

6. The optical system of any of Embodiments 1-5, wherein each of thefirst nanobeams have a same width.

7. The optical system of any of Embodiments 1-6, wherein each of thesecond nanobeams has a same width.

8. The optical system of any of Embodiments 1-7, wherein each of thefirst nanobeams in each of the second nanobeams have a same spacingbetween individual ones of the first and second nanobeams.

9. The optical system of any of Embodiments 1-7, wherein the unit cellsrepeat at a period less than or equal to the wavelength, wherein thewavelength is within the visible spectrum.

10. The optical system of any of Embodiments 1-9, wherein the one ormore first nanobeams and the second nanobeams have a height smaller thanthe wavelength.

11. The optical system of any of Embodiments 1-10, wherein the one ormore first nanobeams and the second nanobeams are formed of a materialwhose bulk refractive index is higher than 2.0 at the wavelength.

12. The optical system of any of Embodiments 1-11, wherein the one ormore first nanobeams and the second nanobeams are formed of asemiconductor material or an insulating material.

13. The optical system of any of Embodiments 1-12, wherein the one ormore first nanobeams and the second nanobeams are formed of a materialhaving silicon.

14. The optical system of any of Embodiments 1-13, wherein the one ormore first nanobeams and the second nanobeams are formed of a materialselected from the group consisting of polycrystalline silicon, amorphoussilicon, silicon carbide and silicon nitride.

15. The optical system of any of Embodiments 1-14, wherein the one ormore first nanobeams and the second nanobeams are configured to diffractthe visible light at a diffraction efficiency greater than 10% at adiffraction angle greater than 50 degrees relative to a surface normalplane.

16. The optical system of Embodiment 15, wherein the one or more firstnanobeams and the second nanobeams are configured to diffract light atthe diffraction efficiency for the incident light having a range ofangle of incidence which exceeds 40 degrees.

17. The optical system of Embodiment 16, wherein the surface normalplane extends in the first orientation direction.

18. The optical system of Embodiment 17, wherein the one or more firstnanobeams and the second nanobeams are configured to diffract light in atransmission mode, wherein the intensity of diffracted light on anopposite side of the one or more first nanobeams and the secondnanobeams as a light-incident side is greater compared to the intensityof diffracted light on a same side of the one or more first nanobeamsand the second nanobeams as the light-incident side.

19. The optical system of Embodiment 17, wherein the wherein the one ormore first nanobeams and the second nanobeams are configured to diffractlight in a reflection mode, wherein the intensity of diffracted light ona same side of the one or more first nanobeams and the second nanobeamsas a light-incident side is greater compared to the intensity ofdiffracted light on an opposite side of the one or more first nanobeamsand the second nanobeams as the light-incident side.

20. The optical system of any of Embodiments 1-19, wherein the one ormore first nanobeams and the second nanobeams are formed on a substrateand formed of a material whose bulk refractive index is greater than arefractive index of the substrate by at least 0.5.

21. The optical system of Embodiment 20, wherein the substrate has arefractive index greater than 1.5.

22. The optical system of any of Embodiments 20-21, wherein thesubstrate is configured such that light diffracted by the one or morefirst nanobeams and the second nanobeams propagate in the seconddirection under total internal reflection.

23. The optical system of any of Embodiments 1-22, wherein the one ormore first nanobeams and the second nanobeams have a substantiallyrectangular cross-sectional shape.

24. The optical system of any of Embodiments 1-23, wherein the one ormore first nanobeams comprise a pair of first nanobeams.

25. The optical system of Embodiment 24, wherein the one or more firstnanobeams are immediately adjacent to the pair of nanobeams such thatthe second nanobeams are directly interposed between adjacent pairs offirst nanobeams.

26. The optical system of any of Embodiments 1-23, wherein the one ormore first nanobeams consists of one first nanobeam.

27. The optical system of any of Embodiments 1-24 and 26, furthercomprising a third set of nanobeams formed by a plurality of thirdnanobeams elongated in a different orientation relative to the first oneor more first nanobeams and the plurality of second nanobeams, the thirdnanobeams interposed between the one or more first nanobeams and thesecond nanobeams.

28. The optical system of Embodiment 27, wherein the third nanobeamshave the same length such that the third nanobeams coterminate.

29. The optical system of any of Embodiments 27-28, wherein adjacentones of the third nanobeams are separated by a constant space in thefirst orientation direction.

30. The optical system of any of Embodiments 27-29, wherein the one ormore first nanobeams span a distance in the first orientation directioncorresponding to a plurality of third nanobeams.

31. The optical system of any of Embodiments 27-30, wherein each of thethird nanobeams has the same width and wherein a spacing betweenindividual ones of the third has a same width.

32. The optical system of any of Embodiments 27-31, wherein the thirdnanobeams extend in a third orientation direction that is rotated in acounterclockwise direction relative to the one or more first nanobeamsby an angle smaller than the smallest angle of rotation in thecounterclockwise direction of the second nanobeams relative to the oneor more first nanobeams when viewed a direction of propagation of anincident light.

33. The optical system of any of Embodiments 27-32, further comprising afourth set of nanobeams formed by a plurality of fourth nanobeamselongated in a different orientation relative to the first one or morefirst nanobeams, the plurality of second nanobeams and the plurality ofthird nanobeams, the fourth nanobeams disposed on a side of the secondnanobeams in the second orientation direction that is opposite to a sidein which the third nanobeams are disposed.

34. The optical system of any of Embodiments 33, wherein the fourthnanobeams extend in a fourth orientation direction that is rotated in acounterclockwise direction relative to the one or more first nanobeamsby an angle greater than the smallest angle of rotation in thecounterclockwise direction of the second nanobeams relative to the oneor more first nanobeams when viewed a direction of propagation of anincident light.

35. The optical system of Embodiment 34, wherein the fourth orientationdirection and the third orientation direction are rotated by about 90degrees relative to each other.

36. The optical system of any of Embodiments 1-35, wherein the one ormore first nanobeams and the second nanobeams comprise a bilayercomprising a lower layer having a first refractive index and an upperlayer having a second refractive index lower than the first refractiveindex.

37. The optical system of Embodiment 36, wherein the upper layer isformed of a material having a refractive index lower than about 2.0.

38. The optical system of any of Embodiments 36-37, wherein the upperlayer contains silicon or carbon.

39. The optical system of any of Embodiments 1-38, wherein the one ormore first nanobeams and the second nanobeams are buried in atransparent spacer layer.

40. The optical system of Embodiment 39, wherein the transparent spacerlayer has a refractive index smaller than a refractive index of a bulkmaterial of one or more first nanobeams and the second nanobeams.

41. The optical system of any of Embodiments 1-38, wherein a metallicreflective layer is formed over the one or more first nanobeams and thesecond nanobeams.

42. An optical system comprising:

-   -   a waveguide configured to propagate visible light, the wave        guide comprising:        -   a substrate having thereon a metasurface according to any of            Embodiments 1-41, wherein the one or more first nanobeams            and the second nanobeams are arranged to diffract light at a            diffraction angle relative to the direction of an incident            light and to cause the diffracted light to propagate in the            substrate under total internal reflection. 43. The waveguide            of Embodiment 42, wherein the substrate is formed of a            material whose refractive index is less than a bulk            refractive index of the material from which the one or more            nanobeams and the second nanobeams are formed, thereby            causing the diffracted light to propagate in the substrate            under total internal reflection.

44. The waveguide of any of Embodiments 42-43, wherein the diffractionangle exceeds 50 degrees.

45. The waveguide of any of Embodiment 42-44, wherein the substrate isformed of a material whose refractive index is smaller than a bulkrefractive index of the material from which the one or more nanobeamsand the second nanobeams are formed by at least 0.5.

46. The waveguide of any of Embodiments 42-45, wherein the substrate hasa refractive index greater than 1.5.

47. A head-mounted display device configured to project light to an eyeof a user to display augmented reality image content, the head-mounteddisplay device comprising:

-   -   a frame configured to be supported on a head of the user;    -   a display disposed on the frame, at least a portion of the        display comprising:        -   one or more waveguides, the one or more waveguides being            transparent and disposed at a location in front of the            user's eye when the user wears the head-mounted display            device such that the transparent portion transmits light            from a portion of an environment in front of the user to the            user's eye to provide a view of the portion of the            environment in front of the user;        -   one or more light sources; and        -   at least one diffraction grating configured to couple light            from the light sources into the one or more waveguides or to            couple light out of the one or more waveguides, the            diffraction grating comprising a metasurface according to            any of Embodiments 1-41.

48. The device of Embodiment 47, wherein the one or more light sourcescomprises a fiber scanning projector.

49. The device of any of Embodiments 47-48, the display configured toproject light into the user's eye so as to present image content to theuser on a plurality of depth planes.

50. A method of fabricating an optical system, comprising:

-   -   providing a substrate;    -   forming on the substrate a metasurface comprising a plurality of        unit cells, the unit cells consisting of two to four sets of        nanobeams, wherein forming the unit cells comprises:        -   forming a first set of nanobeams comprising one or more            first nanobeams; and        -   forming a second set of nanobeams adjacent to the one or            more first nanobeams, the second set of nanobeams comprising            a plurality of second nanobeams that are separated from each            other by a sub-wavelength spacing,        -   wherein the one or more first nanobeams and the plurality of            second nanobeams are elongated in different orientation            directions, and        -   wherein the unit cells repeat at a period less than or equal            to about 10 nm to 1 μm.

51. The method of Embodiment 50, wherein forming the one or more firstnanobeams and forming the second nanobeams comprises lithographicallydefining the first and second nanobeams.

52. The method of Embodiment 50, wherein forming the one or more firstnanobeams and forming the second nanobeams comprises forming the firstand second nanobeams by nanoimprinting.

53. The method of any of Embodiments 50-52, wherein forming the one ormore first nanobeams and forming the second nanobeams are performedsimultaneously.

54. The method of any of Embodiments 50-53, wherein the one or morefirst nanobeams have the same width.

55. The method of any of Embodiments 50-54, wherein the second nanobeamsof each unit cell have the same width.

56. The method of any of Embodiments 50-55, wherein the units cells havea period less than or equal to a wavelength in the visible spectrum.

57. An optical system comprising:

-   -   a metasurface configured to diffract visible light having a        wavelength, the metasurface comprising:        -   a plurality of repeating unit cells, each unit cell            comprising:            -   a first set of nanobeams formed by one or more first                nanobeams; and            -   a second set of nanobeams formed by a plurality of                second nanobeams disposed adjacent to the one or more                first nanobeams and separated from each other by a                sub-wavelength spacing,            -   wherein the one or more first nanobeams and the                plurality of second nanobeams are elongated in different                orientation directions, and            -   wherein the unit cells repeat at a period less than or                equal to the wavelength.

58. The optical system of Embodiment 57, further comprising a lightsource configured to emit light of the wavelength to the metasurface.

59. The optical system of Embodiment 58, further comprising a spatiallight modulator configured to modulate light from the light source andto output the modulated light to the metasurface.

60. The optical system of any of Embodiments 57-59, wherein thewavelength corresponds to blue light, green light or red light.

61. An optical system comprising:

-   -   a metasurface configured to diffract visible light having a        wavelength, the metasurface comprising:        -   a plurality of repeating unit cells, each unit cell            comprising:            -   a first set of nanobeams, wherein two or more of the                first nanobeams have different widths; and            -   a second set of nanobeams, wherein two or more of the                second nanobeams have different widths, the second                nanobeams disposed adjacent to the first nanobeams and                separated from each other by a sub-wavelength spacing,            -   wherein the first nanobeams and the second nanobeams                have different orientations.

62. The optical system of Embodiment 61, further comprising a lightsource configured to emit light of the wavelength to the metasurface.

63. The optical system of Embodiment 62, further comprising a spatiallight modulator configured to modulate light from the light source andto output the modulated light to the metasurface.

64. The optical system of any of Embodiments 61-63, wherein thewavelength corresponds to blue light, green light, or red light.

65. The optical system of Embodiment 61, wherein the first set ofnanobeams and the second set of nanobeams are arranged such that themetasurface is configured to diffract visible light into a single orderof diffracted light.

66. The optical system of any of Embodiments 61-65, wherein the firstset of nanobeams comprises a pair of first nanobeams having a firstwidth and a second width, respectively, and wherein the second set ofnanobeams comprises alternating second nanobeams having a third widthand a fourth width.

67. The optical system of any of Embodiments 61-66, wherein the unitcells repeat at a period less than or equal to about 10 nm to 1 μm.

68. The optical system of any of Embodiments 61-68, wherein the unitcells repeat at a period less than or equal to the wavelength, whereinthe wavelength is within the visible spectrum.

69. The optical system of any of Embodiments 61-68, wherein the firstnanobeams and the second nanobeams are oriented at an angle oforientation relative to each other to cause a phase difference betweenvisible light diffracted by the first set of nanobeams and the visiblelight diffracted by the second set of nanobeams.

70. The optical system of Embodiment 69, wherein the phase difference istwice the angle.

71. The optical system of any of Embodiments 69-70, wherein the angle oforientation is about 90 degrees.

72. The optical system of any of Embodiments 61-67, wherein the firstnanobeams and the second nanobeams have a height smaller than thewavelength.

73. The optical system of any of Embodiments 61-72, wherein the firstnanobeams and the second nanobeams are formed of a material whose bulkrefractive index is higher than 2.0 at the wavelength.

74. The optical system of any of Embodiments 61-73, wherein the firstnanobeams and the second nanobeams are formed of a semiconductormaterial or an insulating material.

75. The optical system of any of Embodiments 61-74, wherein the firstnanobeams and the second nanobeams are formed of titanium dioxide.

76. The optical system of any of Embodiments 61-75, wherein the firstnanobeams and the second nanobeams are formed of a silicon-containingmaterial.

77. The optical system of any of Embodiments 61-76, wherein the firstnanobeams and the second nanobeams are formed of a material selectedfrom the group consisting of monocrystalline silicon, polycrystallinesilicon, amorphous silicon, silicon carbide and silicon nitride.

78. The optical system of any of Embodiments 61-77, wherein the firstnanobeams and the second nanobeams are configured to diffract visiblelight at a diffraction efficiency greater than 10% at a diffractionangle greater than 50 degrees relative to a surface normal plane.

79. The optical system of Embodiment 78, wherein the first nanobeams andthe second nanobeams are configured to diffract light at the diffractionefficiency for the incident light having a range of angles of incidencewhich exceeds 40 degrees.

80. The optical system of Embodiment 79, wherein the surface normalplane extends in the first orientation direction.

81. The optical system of Embodiment 80, wherein the first nanobeams andthe second nanobeams are configured to diffract light in a transmissionmode, wherein the intensity of diffracted light on an opposite side ofthe first nanobeams and the second nanobeams as a light-incident side isgreater compared to the intensity of diffracted light on a same side ofthe first nanobeams and the second nanobeams as the light-incident side.

82. The optical system of Embodiment 80, wherein the first nanobeams andthe second nanobeams are configured to diffract light in a reflectionmode, wherein the intensity of diffracted light on a same side of thefirst nanobeams and the second nanobeams as a light-incident side isgreater compared to the intensity of diffracted light on an oppositeside of the first nanobeams and the second nanobeams as thelight-incident side.

83. The optical system of any of Embodiments 61-82, wherein the firstnanobeams and the second nanobeams are formed on a substrate and formedof a material whose bulk refractive index is greater than a refractiveindex of the substrate by at least 0.5.

84. The optical system of Embodiment 83, wherein the substrate has arefractive index greater than 1.5.

85. The optical system of any of Embodiments 83-84, wherein thesubstrate is configured such that light diffracted by the firstnanobeams and the second nanobeams propagate in the second directionunder total internal reflection.

86. The optical system of any of Embodiments 61-85, wherein the firstnanobeams and the second nanobeams have a substantially rectangularcross-sectional shape.

87. The optical system of any of Embodiments 61-85, wherein the firstnanobeams are immediately adjacent to a pair of nanobeams such that thesecond nanobeams are directly interposed between adjacent pairs of firstnanobeams.

88. The optical system of any of Embodiments 61-87, further comprising awaveguide configured to propagate visible light, wherein the metasurfaceis disposed over the waveguide, wherein the metasurface comprises thefirst nanobeams and the second nanobeams arranged to diffract light at adiffraction angle relative to an incident direction of light to causethe diffracted light to propagate in the substrate under total internalreflection.

89. The optical system of any of Embodiment 61-88, wherein the substrateis formed of a material whose refractive index is smaller than a bulkrefractive index of the material from which the first nanobeams and thesecond nanobeams are formed by at least 0.5.

90. A head-mounted display device configured to project light to an eyeof a user to display augmented reality image content, the head-mounteddisplay device comprising:

-   -   a frame configured to be supported on a head of the user;    -   a display disposed on the frame, at least a portion of the        display comprising:        -   one or more waveguides, the one or more waveguides being            transparent and disposed at a location in front of the            user's eye when the user wears the head-mounted display            device such that the transparent portion transmits light to            the user's eye to provide a view of the portion of the            environment in front of the user;        -   one or more light sources; and        -   at least one diffraction grating configured to couple light            from the light sources into the one or more waveguides or to            couple light out of the one or more waveguides, the            diffraction grating comprising a metasurface according to            any of Embodiments 61-87.

91. The display device of Embodiment 90, wherein the one or more lightsources comprises a fiber scanning projector.

92. The display device of any of Embodiments 90-91, wherein the displayis configured to project light into the user's eye so as to presentimage content to the user on a plurality of depth planes.

93. A method of fabricating a metasurface, comprising:

-   -   providing a substrate;    -   forming on the substrate a metasurface having a plurality of        unit cells, forming the metasurface comprising:        -   forming a first set of nanobeams comprising two or more            first nanobeams having different widths; and        -   forming a second set of nanobeams comprising two or more            second nanobeams having different widths, the second            nanobeams disposed adjacent to the first nanobeams and            separated from each other by a sub-wavelength spacing,        -   wherein the first nanobeams and the second nanobeams have            different orientations.

94. The method of Embodiment 93, wherein forming the first nanobeams andforming the second nanobeams comprises simultaneously lithographicallydefining the first and second nanobeams.

95. The method of Embodiment 93, wherein forming the first nanobeams andforming the second nanobeams comprises forming the first and secondnanobeams by nanoimprinting.

96. The method of any of Embodiments 93-95, wherein forming the firstnanobeams and forming the second nanobeams are performed simultaneously.

97. The method of any of Embodiments 93-96, wherein the units cells havea periodicity less than or equal to a wavelength in the visiblespectrum.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a user's view of augmented reality (AR) through an ARdevice.

FIG. 2 illustrates an example of wearable display system.

FIG. 3 illustrates a conventional display system for simulatingthree-dimensional imagery for a user.

FIG. 4 illustrates aspects of an approach for simulatingthree-dimensional imagery using multiple depth planes.

FIGS. 5A-5C illustrate relationships between radius of curvature andfocal radius.

FIG. 6 illustrates an example of a waveguide stack for outputting imageinformation to a user.

FIG. 7 illustrates an example of exit beams outputted by a waveguide.

FIG. 8 illustrates an example of a stacked waveguide assembly in whicheach depth plane includes images formed using multiple differentcomponent colors.

FIG. 9A illustrates a cross-sectional side view of an example of a setof stacked waveguides that each includes an incoupling optical element.

FIG. 9B illustrates a perspective view of an example of the plurality ofstacked waveguides of FIG. 9A.

FIG. 9C illustrates a top-down plan view of an example of the pluralityof stacked waveguides of FIGS. 9A and 9B.

FIG. 10A schematically illustrates a cross-sectional view of an axiconas an example of a conventional optical element.

FIG. 10B schematically illustrates a cross-sectional view of ametasurface-based axicon as an example of an optical element formed of ametasurface.

FIG. 10C illustrates the transmitted beam profile resulting when themetasurface-based axicon of FIG. 10B is illuminated with a collimatedGaussian left circularly polarized (LCP) light beam.

FIG. 11A illustrates an example waveplate formed of a metasurfacecomprising a plurality of nanobeams, under top-down illumination byincident light having a transverse electric (TE) polarization and anorthogonal transverse magnetic (TM) polarization.

FIG. 11B illustrates simulated phase wavefronts resulting from theexample waveplate illustrated with reference to FIG. 11A

FIG. 11C illustrates simulated phase retardation of a TM-polarized lightwith respect to a TE-polarized light beam resulting from the examplewaveplate of FIG. 11A.

FIG. 11D illustrates simulated absorption spectra of the examplewaveplate of FIG. 11A, corresponding to the simulated phase retardationillustrated in FIG. 11C.

FIGS. 12A-12H illustrate changes in polarization vectors of an incidentlight corresponding to rotations in the fast axes of a waveplate by anangle θ of 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2 and 7π/4, respectively.

FIGS. 13A and 13B illustrate a cross-sectional side view and a top-downview, respectively, of a diffraction grating comprising a metasurfacehaving 2-phase level geometric phase optical elements, according to someembodiments.

FIG. 14 illustrates a simulated diffraction efficiency versus angle ofincidence (α) for an exemplary diffraction grating described withreference to FIGS. 13A and 13B.

FIGS. 15A and 15B illustrate two-dimensional simulations of phasewavefronts for TE-polarized light upon transmission through thediffraction grating described with reference to FIGS. 13A and 13B.

FIG. 16A illustrates a cross-sectional side view of a diffractiongrating comprising a metasurface having geometric phase opticalelements, according to some embodiments, in which a masking layer isleft-in, according to some embodiments.

FIG. 16B illustrates simulated diffraction efficiency (η) versus thethickness of the masking layer for the exemplary diffraction gratingillustrated in FIG. 16A.

FIG. 16C illustrates simulated diffraction efficiency (η) versus angleof incidence (α) for an exemplary diffraction grating illustrated inFIG. 16A, in which the left-in masking layer is 20 nm thick, accordingto some embodiments.

FIG. 16D illustrates simulated diffraction efficiency (η) versus angleof incidence (α) for an exemplary diffraction grating illustrated inFIG. 16A, in which the left-in masking layer is 40 nm thick, accordingto some embodiments.

FIGS. 17A and 17B illustrate simulated diffraction efficiencies (η)versus angle of incidence (α) for an exemplary diffraction gratingformed of amorphous silicon, for TE and TM polarized green light,respectively, according to some embodiments.

FIG. 18 illustrates simulated diffraction efficiency (η) versus angle ofincidence (α) for an exemplary diffraction grating formed ofpolycrystalline silicon and configured to diffract green light,according to some embodiments.

FIG. 19 illustrates simulated diffraction efficiency (η) versus angle ofincidence (α) for an exemplary diffraction grating formed of siliconcarbide (SiC) and configured to diffract green light, according to someembodiments.

FIG. 20 illustrates simulated diffraction efficiency (η) versus angle ofincidence (α) for an exemplary diffraction grating formed of siliconnitride (Si₃N₄) and configured to diffract green light, according tosome embodiments.

FIG. 21 illustrates simulated diffraction efficiency (η) versus angle ofincidence (α) for an exemplary diffraction grating formed ofpolycrystalline silicon and configured to diffract blue light, accordingto some embodiments.

FIG. 22 illustrates simulated diffraction efficiency (η) versus angle ofincidence (α) for an exemplary diffraction grating formed of amorphoussilicon and configured to diffract blue light, according to someembodiments.

FIG. 23 illustrates simulated diffraction efficiency (η) versus angle ofincidence (α) for an exemplary diffraction grating formed of siliconcarbide (SiC) and configured to diffract blue light, according to someembodiments.

FIG. 24 illustrates simulated diffraction efficiency (η) versus angle ofincidence (α) for an exemplary diffraction grating formed of siliconnitride (Si₃N₄) and configured to diffract blue light, according to someembodiments.

FIG. 25 illustrates a top-down view of a diffraction grating comprisinga metasurface having 4-phase level geometric phase optical elements,according to some embodiments.

FIG. 26 illustrates a cross-sectional view of a diffraction gratingcomprising a metasurface having geometric phase optical elements,configured to diffract in reflective mode, according to someembodiments.

FIG. 27 illustrates a simulated diffraction efficiency (η) versus angleof incidence (α) for an exemplary diffraction illustrated in FIG. 26.

FIGS. 28A-28D are cross-sectional views of intermediate structures atvarious stages of fabrication of a diffraction grating comprising ametasurface having geometric phase optical elements, according to someembodiments.

FIGS. 29A-29D are cross-sectional views of intermediate structures atvarious stages of fabrication of a diffraction grating comprising ametasurface having geometric phase optical elements, according to someother embodiments.

FIGS. 30A and 30B illustrate a cross-sectional side view and a top-downview, respectively, of a diffraction grating comprising a metasurfacehaving 2-phase level, asymmetric geometric phase optical elements,according to some embodiments.

FIGS. 31A and 31B illustrate simulated diffraction efficiencies (η)versus angle of incidence (α) for an exemplary diffraction gratingformed of polycrystalline silicon, for TE and TM polarized green light,respectively, according to some embodiments.

FIGS. 32A and 32B illustrate simulated diffraction efficiencies (η)versus angle of incidence (α) for an exemplary diffraction gratingformed of amorphous silicon, for TE and TM polarized green light,respectively, according to some embodiments

FIGS. 33A and 33B illustrate simulated diffraction efficiencies (η)versus angle of incidence (α) for an exemplary diffraction gratingformed of amorphous silicon, for TE and TM polarized green light,respectively, according to some embodiments.

DETAILED DESCRIPTION

Optical systems, such as display systems, often utilize optical elementsto control the propagation of light. In some applications, due to demandfor compact optical systems, conventional optical elements may no longerbe suitable.

Metasurfaces, metamaterial surfaces, provide opportunities to realizevirtually flat, aberration-free optics on much smaller scales, incomparison with geometrical optics. Without being limited by theory, insome embodiments, metasurfaces include dense arrangements of surfacestructures that function as resonant optical antennas. The resonantnature of the light-surface structure interaction provides the abilityto manipulate optical wave-fronts. In some cases, the metasurfaces mayallow the replacement of bulky or difficult to manufacture opticalcomponents with thin, relatively planar elements formed by simplepatterning processes.

In some embodiments, metasurfaces for forming diffractive gratings aredisclosed. The metasurfaces may take the form of a grating formed by aplurality of repeating unit cells. Each unit cell may comprise two setsor more of nanobeams elongated in crossing directions: one or more firstnanobeams elongated in a first direction and a plurality of secondnanobeams elongated in a second direction different from the firstdirection. For example, as seen in a top-down view, the first directionmay be generally along a y-axis, and the second direction may begenerally along an x-axis. In some embodiments, the unit cells maycomprise four sets of nanobeams: one or more first nanobeams elongatedin the first direction, a plurality of second nanobeams elongated in thesecond direction, a plurality of third nanobeams elongated in a thirddirection, and a plurality of fourth nanobeams elongated in a fourthdirection. As an example, the first and second directions may form afirst angle relative to one another (e.g., 90°), and the first and thirddirections and first and fourth directions may form opposite angles toone another. In some embodiments, the metasurfaces may be symmetric inthe sense that each of the first nanobeams, where there are multiplefirst nanobeams, have the same width. In some other embodiments, themetasurfaces may be described as being asymmetric in the sense that atleast one of the first nanobeams in a unit cell, where there aremultiple first nanobeams, has a different width from at least one otherof the first nanobeams. In some embodiments, the unit cells of thesymmetric or asymmetric metasurfaces have a periodicity in the range of10 nm to 1 μm, including 10 nm to 500 nm or 300 nm to 500 nm, and may beless than the wavelengths of light that the metasurface is configured todiffract or which are directed to the metasurface for, e.g., incouplinginto or outcoupling out of a waveguide. Advantageously, as it has beenfound that the metasurfaces disclosed herein provide diffraction oflight with high diffraction angles and high diffraction efficienciesover a broad range of incident angles and for incident light withcircular polarization. In particular, in some embodiments, asymmetricmetasurfaces can steer the diffracted light into one of a plurality ofdiffraction orders while reducing the other(s) of the plurality ofdiffraction orders. In addition, in some embodiments, the metasurfacesdiffract light with high wavelength selectivity.

In some embodiments, the metasurfaces may be utilized in wearabledisplay systems to provide compact optical elements. AR systems maydisplay virtual content to a user, or viewer, while still allowing theuser to see the world around them. Preferably, this content is displayedon a head-mounted display, e.g., as part of eyewear, that projects imageinformation to the user's eyes. In addition, the display may alsotransmit light from the surrounding environment to the user's eyes, toallow a view of that surrounding environment. As used herein, it will beappreciated that a “head-mounted” display is a display that may bemounted on the head of a viewer.

Reference will now be made to the drawings, in which like referencenumerals refer to like parts throughout.

Example Display Systems

FIG. 2 illustrates an example of wearable display system 60. The displaysystem 60 includes a display 70, and various mechanical and electronicmodules and systems to support the functioning of that display 70. Thedisplay 70 may be coupled to a frame 80, which is wearable by a displaysystem user or viewer 90 and which is configured to position the display70 in front of the eyes of the user 90. The display 70 may be consideredeyewear in some embodiments. In some embodiments, a speaker 100 iscoupled to the frame 80 and configured to be positioned adjacent the earcanal of the user 90 (in some embodiments, another speaker, not shown,may optionally be positioned adjacent the other ear canal of the user toprovide stereo/shapeable sound control). The display system may alsoinclude one or more microphones 110 or other devices to detect sound. Insome embodiments, the microphone is configured to allow the user toprovide inputs or commands to the system 60 (e.g., the selection ofvoice menu commands, natural language questions, etc.), and/or may allowaudio communication with other persons (e.g., with other users ofsimilar display systems. The microphone may further be configured as aperipheral sensor to collect audio data (e.g., sounds from the userand/or environment). In some embodiments, the display system may alsoinclude a peripheral sensor 120 a, which may be separate from the frame80 and attached to the body of the user 90 (e.g., on the head, torso, anextremity, etc. of the user 90). The peripheral sensor 120 a may beconfigured to acquire data characterizing a physiological state of theuser 90 in some embodiments. For example, the sensor 120 a may be anelectrode.

With continued reference to FIG. 2, the display 70 is operativelycoupled by communications link 130, such as by a wired lead or wirelessconnectivity, to a local data processing module 140 which may be mountedin a variety of configurations, such as fixedly attached to the frame80, fixedly attached to a helmet or hat worn by the user, embedded inheadphones, or otherwise removably attached to the user 90 (e.g., in abackpack-style configuration, in a belt-coupling style configuration).Similarly, the sensor 120 a may be operatively coupled by communicationslink 120 b, e.g., a wired lead or wireless connectivity, to the localprocessor and data module 140. The local processing and data module 140may comprise a hardware processor, as well as digital memory, such asnon-volatile memory (e.g., flash memory or hard disk drives), both ofwhich may be utilized to assist in the processing, caching, and storageof data. The data include data a) captured from sensors (which may be,e.g., operatively coupled to the frame 80 or otherwise attached to theuser 90), such as image capture devices (such as cameras), microphones,inertial measurement units, accelerometers, compasses, GPS units, radiodevices, gyros, and/or other sensors disclosed herein; and/or b)acquired and/or processed using remote processing module 150 and/orremote data repository 160 (including data relating to virtual content),possibly for passage to the display 70 after such processing orretrieval. The local processing and data module 140 may be operativelycoupled by communication links 170, 180, such as via a wired or wirelesscommunication links, to the remote processing module 150 and remote datarepository 160 such that these remote modules 150, 160 are operativelycoupled to each other and available as resources to the local processingand data module 140. In some embodiments, the local processing and datamodule 140 may include one or more of the image capture devices,microphones, inertial measurement units, accelerometers, compasses, GPSunits, radio devices, and/or gyros. In some other embodiments, one ormore of these sensors may be attached to the frame 80, or may bestandalone structures that communicate with the local processing anddata module 140 by wired or wireless communication pathways.

With continued reference to FIG. 2, in some embodiments, the remoteprocessing module 150 may comprise one or more processors configured toanalyze and process data and/or image information. In some embodiments,the remote data repository 160 may comprise a digital data storagefacility, which may be available through the internet or othernetworking configuration in a “cloud” resource configuration. In someembodiments, the remote data repository 160 may include one or moreremote servers, which provide information, e.g., information forgenerating augmented reality content, to the local processing and datamodule 140 and/or the remote processing module 150. In some embodiments,all data is stored and all computations are performed in the localprocessing and data module, allowing fully autonomous use from a remotemodule.

With reference now to FIG. 3, the perception of an image as being“three-dimensional” or “3-D” may be achieved by providing slightlydifferent presentations of the image to each eye of the viewer. FIG. 3illustrates a conventional display system for simulatingthree-dimensional imagery for a user. Two distinct images 190, 200—onefor each eye 210, 220—are outputted to the user. The images 190, 200 arespaced from the eyes 210, 220 by a distance 230 along an optical orz-axis that is parallel to the line of sight of the viewer. The images190, 200 are flat and the eyes 210, 220 may focus on the images byassuming a single accommodated state. Such 3-D display systems rely onthe human visual system to combine the images 190, 200 to provide aperception of depth and/or scale for the combined image.

It will be appreciated, however, that the human visual system is morecomplicated and providing a realistic perception of depth is morechallenging. For example, many viewers of conventional “3-D” displaysystems find such systems to be uncomfortable or may not perceive asense of depth at all. Without being limited by theory, it is believedthat viewers of an object may perceive the object as being“three-dimensional” due to a combination of vergence and accommodation.Vergence movements (i.e., rotation of the eyes so that the pupils movetoward or away from each other to converge the lines of sight of theeyes to fixate upon an object) of the two eyes relative to each otherare closely associated with focusing (or “accommodation”) of the lensesand pupils of the eyes. Under normal conditions, changing the focus ofthe lenses of the eyes, or accommodating the eyes, to change focus fromone object to another object at a different distance will automaticallycause a matching change in vergence to the same distance, under arelationship known as the “accommodation-vergence reflex,” as well aspupil dilation or constriction. Likewise, a change in vergence willtrigger a matching change in accommodation of lens shape and pupil size,under normal conditions. As noted herein, many stereoscopic or “3-D”display systems display a scene using slightly different presentations(and, so, slightly different images) to each eye such that athree-dimensional perspective is perceived by the human visual system.Such systems are uncomfortable for many viewers, however, since they,among other things, simply provide different presentations of a scene,but with the eyes viewing all the image information at a singleaccommodated state, and work against the “accommodation-vergencereflex.” Display systems that provide a better match betweenaccommodation and vergence may form more realistic and comfortablesimulations of three-dimensional imagery.

FIG. 4 illustrates aspects of an approach for simulatingthree-dimensional imagery using multiple depth planes. With reference toFIG. 4, objects at various distances from eyes 210, 220 on the z-axisare accommodated by the eyes 210, 220 so that those objects are infocus. The eyes 210, 220 assume particular accommodated states to bringinto focus objects at different distances along the z-axis.Consequently, a particular accommodated state may be said to beassociated with a particular one of depth planes 240, with has anassociated focal distance, such that objects or parts of objects in aparticular depth plane are in focus when the eye is in the accommodatedstate for that depth plane. In some embodiments, three-dimensionalimagery may be simulated by providing different presentations of animage for each of the eyes 210, 220, and also by providing differentpresentations of the image corresponding to each of the depth planes.While shown as being separate for clarity of illustration, it will beappreciated that the fields of view of the eyes 210, 220 may overlap,for example, as distance along the z-axis increases. In addition, whileshown as flat for ease of illustration, it will be appreciated that thecontours of a depth plane may be curved in physical space, such that allfeatures in a depth plane are in focus with the eye in a particularaccommodated state.

The distance between an object and the eye 210 or 220 may also changethe amount of divergence of light from that object, as viewed by thateye. FIGS. 5A-5C illustrate relationships between distance and thedivergence of light rays. The distance between the object and the eye210 is represented by, in order of decreasing distance, R1, R2, and R3.As shown in FIGS. 5A-5C, the light rays become more divergent asdistance to the object decreases. As distance increases, the light raysbecome more collimated. Stated another way, it may be said that thelight field produced by a point (the object or a part of the object) hasa spherical wavefront curvature, which is a function of how far away thepoint is from the eye of the user. The curvature increases withdecreasing distance between the object and the eye 210. Consequently, atdifferent depth planes, the degree of divergence of light rays is alsodifferent, with the degree of divergence increasing with decreasingdistance between depth planes and the viewer's eye 210. While only asingle eye 210 is illustrated for clarity of illustration in FIGS. 5A-5Cand other figures herein, it will be appreciated that the discussionsregarding eye 210 may be applied to both eyes 210 and 220 of a viewer.

Without being limited by theory, it is believed that the human eyetypically can interpret a finite number of depth planes to provide depthperception. Consequently, a highly believable simulation of perceiveddepth may be achieved by providing, to the eye, different presentationsof an image corresponding to each of these limited number of depthplanes. The different presentations may be separately focused by theviewer's eyes, thereby helping to provide the user with depth cues basedon the accommodation of the eye required to bring into focus differentimage features for the scene located on different depth plane and/orbased on observing different image features on different depth planesbeing out of focus.

FIG. 6 illustrates an example of a waveguide stack for outputting imageinformation to a user. A display system 250 includes a stack ofwaveguides, or stacked waveguide assembly, 260 that may be utilized toprovide three-dimensional perception to the eye/brain using a pluralityof waveguides 270, 280, 290, 300, 310. In some embodiments, the displaysystem 250 is the system 60 of FIG. 2, with FIG. 6 schematically showingsome parts of that system 60 in greater detail. For example, thewaveguide assembly 260 may be part of the display 70 of FIG. 2. It willbe appreciated that the display system 250 may be considered a lightfield display in some embodiments.

With continued reference to FIG. 6, the waveguide assembly 260 may alsoinclude a plurality of features 320, 330, 340, 350 between thewaveguides. In some embodiments, the features 320, 330, 340, 350 may beone or more lenses. The waveguides 270, 280, 290, 300, 310 and/or theplurality of lenses 320, 330, 340, 350 may be configured to send imageinformation to the eye with various levels of wavefront curvature orlight ray divergence. Each waveguide level may be associated with aparticular depth plane and may be configured to output image informationcorresponding to that depth plane. Image injection devices 360, 370,380, 390, 400 may function as a source of light for the waveguides andmay be utilized to inject image information into the waveguides 270,280, 290, 300, 310, each of which may be configured, as describedherein, to distribute incoming light across each respective waveguide,for output toward the eye 210. Light exits an output surface 410, 420,430, 440, 450 of the image injection devices 360, 370, 380, 390, 400 andis injected into a corresponding input surface 460, 470, 480, 490, 500of the waveguides 270, 280, 290, 300, 310. In some embodiments, the eachof the input surfaces 460, 470, 480, 490, 500 may be an edge of acorresponding waveguide, or may be part of a major surface of thecorresponding waveguide (that is, one of the waveguide surfaces directlyfacing the world 510 or the viewer's eye 210). In some embodiments, asingle beam of light (e.g. a collimated beam) may be injected into eachwaveguide to output an entire field of cloned collimated beams that aredirected toward the eye 210 at particular angles (and amounts ofdivergence) corresponding to the depth plane associated with aparticular waveguide. In some embodiments, a single one of the imageinjection devices 360, 370, 380, 390, 400 may be associated with andinject light into a plurality (e.g., three) of the waveguides 270, 280,290, 300, 310.

In some embodiments, the image injection devices 360, 370, 380, 390, 400are discrete displays that each produce image information for injectioninto a corresponding waveguide 270, 280, 290, 300, 310, respectively. Insome other embodiments, the image injection devices 360, 370, 380, 390,400 are the output ends of a single multiplexed display which may, e.g.,pipe image information via one or more optical conduits (such as fiberoptic cables) to each of the image injection devices 360, 370, 380, 390,400. It will be appreciated that the image information provided by theimage injection devices 360, 370, 380, 390, 400 may include light ofdifferent wavelengths, or colors (e.g., different component colors, asdiscussed herein).

In some embodiments, the light injected into the waveguides 270, 280,290, 300, 310 is provided by a light projector system 520, whichcomprises a light module 530, which may include a light emitter, such asa light emitting diode (LED). The light from the light module 530 may bedirected to and modified by a light modulator 540, e.g., a spatial lightmodulator, via a beam splitter 550. The light modulator 540 may beconfigured to change the perceived intensity of the light injected intothe waveguides 270, 280, 290, 300, 310. Examples of spatial lightmodulators include liquid crystal displays (LCD) including a liquidcrystal on silicon (LCOS) displays.

In some embodiments, the display system 250 may be a scanning fiberdisplay comprising one or more scanning fibers configured to projectlight in various patterns (e.g., raster scan, spiral scan, Lissajouspatterns, etc.) into one or more waveguides 270, 280, 290, 300, 310 andultimately to the eye 210 of the viewer. In some embodiments, theillustrated image injection devices 360, 370, 380, 390, 400 mayschematically represent a single scanning fiber or a bundle of scanningfibers configured to inject light into one or a plurality of thewaveguides 270, 280, 290, 300, 310. In some other embodiments, theillustrated image injection devices 360, 370, 380, 390, 400 mayschematically represent a plurality of scanning fibers or a plurality ofbundles of scanning fibers, each of which are configured to inject lightinto an associated one of the waveguides 270, 280, 290, 300, 310. Itwill be appreciated that one or more optical fibers may be configured totransmit light from the light module 530 to the one or more waveguides270, 280, 290, 300, 310. It will be appreciated that one or moreintervening optical structures may be provided between the scanningfiber, or fibers, and the one or more waveguides 270, 280, 290, 300, 310to, e.g., redirect light exiting the scanning fiber into the one or morewaveguides 270, 280, 290, 300, 310.

A controller 560 controls the operation of one or more of the stackedwaveguide assembly 260, including operation of the image injectiondevices 360, 370, 380, 390, 400, the light source 530, and the lightmodulator 540. In some embodiments, the controller 560 is part of thelocal data processing module 140. The controller 560 includesprogramming (e.g., instructions in a non-transitory medium) thatregulates the timing and provision of image information to thewaveguides 270, 280, 290, 300, 310 according to, e.g., any of thevarious schemes disclosed herein. In some embodiments, the controllermay be a single integral device, or a distributed system connected bywired or wireless communication channels. The controller 560 may be partof the processing modules 140 or 150 (FIG. 2) in some embodiments.

With continued reference to FIG. 6, the waveguides 270, 280, 290, 300,310 may be configured to propagate light within each respectivewaveguide by total internal reflection (TIR). The waveguides 270, 280,290, 300, 310 may each be planar or have another shape (e.g., curved),with major top and bottom surfaces and edges extending between thosemajor top and bottom surfaces. In the illustrated configuration, thewaveguides 270, 280, 290, 300, 310 may each include out-coupling opticalelements 570, 580, 590, 600, 610 that are configured to extract lightout of a waveguide by redirecting the light, propagating within eachrespective waveguide, out of the waveguide to output image informationto the eye 210. Extracted light may also be referred to as out-coupledlight and the out-coupling optical elements light may also be referredto light extracting optical elements. An extracted beam of light may beoutputted by the waveguide at locations at which the light propagatingin the waveguide strikes a light extracting optical element. Theout-coupling optical elements 570, 580, 590, 600, 610 may, for example,be gratings, including diffractive optical features, as discussedfurther herein. While illustrated disposed at the bottom major surfacesof the waveguides 270, 280, 290, 300, 310, for ease of description anddrawing clarity, in some embodiments, the out-coupling optical elements570, 580, 590, 600, 610 may be disposed at the top and/or bottom majorsurfaces, and/or may be disposed directly in the volume of thewaveguides 270, 280, 290, 300, 310, as discussed further herein. In someembodiments, the out-coupling optical elements 570, 580, 590, 600, 610may be formed in a layer of material that is attached to a transparentsubstrate to form the waveguides 270, 280, 290, 300, 310. In some otherembodiments, the waveguides 270, 280, 290, 300, 310 may be a monolithicpiece of material and the out-coupling optical elements 570, 580, 590,600, 610 may be formed on a surface and/or in the interior of that pieceof material.

With continued reference to FIG. 6, as discussed herein, each waveguide270, 280, 290, 300, 310 is configured to output light to form an imagecorresponding to a particular depth plane. For example, the waveguide270 nearest the eye may be configured to deliver collimated light (whichwas injected into such waveguide 270), to the eye 210. The collimatedlight may be representative of the optical infinity focal plane. Thenext waveguide up 280 may be configured to send out collimated lightwhich passes through the first lens 350 (e.g., a negative lens) beforeit can reach the eye 210; such first lens 350 may be configured tocreate a slight convex wavefront curvature so that the eye/braininterprets light coming from that next waveguide up 280 as coming from afirst focal plane closer inward toward the eye 210 from opticalinfinity. Similarly, the third up waveguide 290 passes its output lightthrough both the first 350 and second 340 lenses before reaching the eye210; the combined optical power of the first 350 and second 340 lensesmay be configured to create another incremental amount of wavefrontcurvature so that the eye/brain interprets light coming from the thirdwaveguide 290 as coming from a second focal plane that is even closerinward toward the person from optical infinity than was light from thenext waveguide up 280.

The other waveguide layers 300, 310 and lenses 330, 320 are similarlyconfigured, with the highest waveguide 310 in the stack sending itsoutput through all of the lenses between it and the eye for an aggregatefocal power representative of the closest focal plane to the person. Tocompensate for the stack of lenses 320, 330, 340, 350 whenviewing/interpreting light coming from the world 510 on the other sideof the stacked waveguide assembly 260, a compensating lens layer 620 maybe disposed at the top of the stack to compensate for the aggregatepower of the lens stack 320, 330, 340, 350 below. Such a configurationprovides as many perceived focal planes as there are availablewaveguide/lens pairings. Both the out-coupling optical elements of thewaveguides and the focusing aspects of the lenses may be static (i.e.,not dynamic or electro-active). In some alternative embodiments, eitheror both may be dynamic using electro-active features.

In some embodiments, two or more of the waveguides 270, 280, 290, 300,310 may have the same associated depth plane. For example, multiplewaveguides 270, 280, 290, 300, 310 may be configured to output imagesset to the same depth plane, or multiple subsets of the waveguides 270,280, 290, 300, 310 may be configured to output images set to the sameplurality of depth planes, with one set for each depth plane. This canprovide advantages for forming a tiled image to provide an expandedfield of view at those depth planes.

With continued reference to FIG. 6, the out-coupling optical elements570, 580, 590, 600, 610 may be configured to both redirect light out oftheir respective waveguides and to output this light with theappropriate amount of divergence or collimation for a particular depthplane associated with the waveguide. As a result, waveguides havingdifferent associated depth planes may have different configurations ofout-coupling optical elements 570, 580, 590, 600, 610, which outputlight with a different amount of divergence depending on the associateddepth plane. In some embodiments, the light extracting optical elements570, 580, 590, 600, 610 may be volumetric or surface features, which maybe configured to output light at specific angles. For example, the lightextracting optical elements 570, 580, 590, 600, 610 may be volumeholograms, surface holograms, and/or diffraction gratings. In someembodiments, the features 320, 330, 340, 350 may not be lenses; rather,they may simply be spacers (e.g., cladding layers and/or structures forforming air gaps).

In some embodiments, the out-coupling optical elements 570, 580, 590,600, 610 are diffractive features that form a diffraction pattern, or“diffractive optical element” (also referred to herein as a “DOE”).Preferably, the DOE's have a sufficiently low diffraction efficiency sothat only a portion of the light of the beam is deflected away towardthe eye 210 with each intersection of the DOE, while the rest continuesto move through a waveguide via TIR. The light carrying the imageinformation is thus divided into a number of related exit beams thatexit the waveguide at a multiplicity of locations and the result is afairly uniform pattern of exit emission toward the eye 210 for thisparticular collimated beam bouncing around within a waveguide.

In some embodiments, one or more DOEs may be switchable between “on”states in which they actively diffract, and “off” states in which theydo not significantly diffract. For instance, a switchable DOE maycomprise a layer of polymer dispersed liquid crystal, in whichmicrodroplets comprise a diffraction pattern in a host medium, and therefractive index of the microdroplets may be switched to substantiallymatch the refractive index of the host material (in which case thepattern does not appreciably diffract incident light) or themicrodroplet may be switched to an index that does not match that of thehost medium (in which case the pattern actively diffracts incidentlight).

In some embodiments, a camera assembly 630 (e.g., a digital camera,including visible light and infrared light cameras) may be provided tocapture images of the eye 210 and/or tissue around the eye 210 to, e.g.,detect user inputs and/or to monitor the physiological state of theuser. As used herein, a camera may be any image capture device. In someembodiments, the camera assembly 630 may include an image capture deviceand a light source to project light (e.g., infrared light) to the eye,which may then be reflected by the eye and detected by the image capturedevice. In some embodiments, the camera assembly 630 may be attached tothe frame 80 (FIG. 2) and may be in electrical communication with theprocessing modules 140 and/or 150, which may process image informationfrom the camera assembly 630. In some embodiments, one camera assembly630 may be utilized for each eye, to separately monitor each eye.

With reference now to FIG. 7, an example of exit beams outputted by awaveguide is shown. One waveguide is illustrated, but it will beappreciated that other waveguides in the waveguide assembly 260 (FIG. 6)may function similarly, where the waveguide assembly 260 includesmultiple waveguides. Light 640 is injected into the waveguide 270 at theinput surface 460 of the waveguide 270 and propagates within thewaveguide 270 by TIR. At points where the light 640 impinges on the DOE570, a portion of the light exits the waveguide as exit beams 650. Theexit beams 650 are illustrated as substantially parallel but, asdiscussed herein, they may also be redirected to propagate to the eye210 at an angle (e.g., forming divergent exit beams), depending on thedepth plane associated with the waveguide 270. It will be appreciatedthat substantially parallel exit beams may be indicative of a waveguidewith out-coupling optical elements that out-couple light to form imagesthat appear to be set on a depth plane at a large distance (e.g.,optical infinity) from the eye 210. Other waveguides or other sets ofout-coupling optical elements may output an exit beam pattern that ismore divergent, which would require the eye 210 to accommodate to acloser distance to bring it into focus on the retina and would beinterpreted by the brain as light from a distance closer to the eye 210than optical infinity.

In some embodiments, a full color image may be formed at each depthplane by overlaying images in each of the component colors, e.g., threeor more component colors. FIG. 8 illustrates an example of a stackedwaveguide assembly in which each depth plane includes images formedusing multiple different component colors. The illustrated embodimentshows depth planes 240 a-240 f, although more or fewer depths are alsocontemplated. Each depth plane may have three or more component colorimages associated with it, including: a first image of a first color, G;a second image of a second color, R; and a third image of a third color,B. Different depth planes are indicated in the figure by differentnumbers for diopters (dpt) following the letters G, R, and B. Just asexamples, the numbers following each of these letters indicate diopters(1/m), or inverse distance of the depth plane from a viewer, and eachbox in the figures represents an individual component color image. Insome embodiments, to account for differences in the eye's focusing oflight of different wavelengths, the exact placement of the depth planesfor different component colors may vary. For example, differentcomponent color images for a given depth plane may be placed on depthplanes corresponding to different distances from the user. Such anarrangement may increase visual acuity and user comfort and/or maydecrease chromatic aberrations.

In some embodiments, light of each component color may be outputted by asingle dedicated waveguide and, consequently, each depth plane may havemultiple waveguides associated with it. In such embodiments, each box inthe figures including the letters G, R, or B may be understood torepresent an individual waveguide, and three waveguides may be providedper depth plane where three component color images are provided perdepth plane. While the waveguides associated with each depth plane areshown adjacent to one another in this drawing for ease of description,it will be appreciated that, in a physical device, the waveguides mayall be arranged in a stack with one waveguide per level. In some otherembodiments, multiple component colors may be outputted by the samewaveguide, such that, e.g., only a single waveguide may be provided perdepth plane.

With continued reference to FIG. 8, in some embodiments, G is the colorgreen, R is the color red, and B is the color blue. In some otherembodiments, other colors associated with other wavelengths of light,including magenta and cyan, may be used in addition to or may replaceone or more of red, green, or blue.

It will be appreciated that references to a given color of lightthroughout this disclosure will be understood to encompass light of oneor more wavelengths within a range of wavelengths of light that areperceived by a viewer as being of that given color. For example, redlight may include light of one or more wavelengths in the range of about620-780 nm, green light may include light of one or more wavelengths inthe range of about 492-577 nm, and blue light may include light of oneor more wavelengths in the range of about 435-493 nm.

In some embodiments, the light source 530 (FIG. 6) may be configured toemit light of one or more wavelengths outside the visual perceptionrange of the viewer, for example, infrared and/or ultravioletwavelengths. In addition, the in-coupling, out-coupling, and other lightredirecting structures of the waveguides of the display 250 may beconfigured to direct and emit this light out of the display towards theuser's eye 210, e.g., for imaging and/or user stimulation applications.

With reference now to FIG. 9A, in some embodiments, light impinging on awaveguide may need to be redirected to in-couple that light into thewaveguide. An in-coupling optical element may be used to redirect andin-couple the light into its corresponding waveguide. FIG. 9Aillustrates a cross-sectional side view of an example of a plurality orset 660 of stacked waveguides that each includes an in-coupling opticalelement. The waveguides may each be configured to output light of one ormore different wavelengths, or one or more different ranges ofwavelengths. It will be appreciated that the stack 660 may correspond tothe stack 260 (FIG. 6) and the illustrated waveguides of the stack 660may correspond to part of the plurality of waveguides 270, 280, 290,300, 310, except that light from one or more of the image injectiondevices 360, 370, 380, 390, 400 is injected into the waveguides from aposition that requires light to be redirected for in-coupling.

The illustrated set 660 of stacked waveguides includes waveguides 670,680, and 690. Each waveguide includes an associated in-coupling opticalelement (which may also be referred to as a light input area on thewaveguide), with, e.g., in-coupling optical element 700 disposed on amajor surface (e.g., an upper major surface) of waveguide 670,in-coupling optical element 710 disposed on a major surface (e.g., anupper major surface) of waveguide 680, and in-coupling optical element720 disposed on a major surface (e.g., an upper major surface) ofwaveguide 690. In some embodiments, one or more of the in-couplingoptical elements 700, 710, 720 may be disposed on the bottom majorsurface of the respective waveguide 670, 680, 690 (particularly wherethe one or more in-coupling optical elements are reflective, deflectingoptical elements). As illustrated, the in-coupling optical elements 700,710, 720 may be disposed on the upper major surface of their respectivewaveguide 670, 680, 690 (or the top of the next lower waveguide),particularly where those in-coupling optical elements are transmissive,deflecting optical elements. In some embodiments, the in-couplingoptical elements 700, 710, 720 may be disposed in the body of therespective waveguide 670, 680, 690. In some embodiments, as discussedherein, the in-coupling optical elements 700, 710, 720 are wavelengthselective, such that they selectively redirect one or more wavelengthsof light, while transmitting other wavelengths of light. Whileillustrated on one side or corner of their respective waveguide 670,680, 690, it will be appreciated that the in-coupling optical elements700, 710, 720 may be disposed in other areas of their respectivewaveguide 670, 680, 690 in some embodiments.

As illustrated, the in-coupling optical elements 700, 710, 720 may belaterally offset from one another. In some embodiments, each in-couplingoptical element may be offset such that it receives light without thatlight passing through another in-coupling optical element. For example,each in-coupling optical element 700, 710, 720 may be configured toreceive light from a different image injection device 360, 370, 380,390, and 400 as shown in FIG. 6, and may be separated (e.g., laterallyspaced apart) from other in-coupling optical elements 700, 710, 720 suchthat it substantially does not receive light from the other ones of thein-coupling optical elements 700, 710, 720.

Each waveguide also includes associated light distributing elements,with, e.g., light distributing elements 730 disposed on a major surface(e.g., a top major surface) of waveguide 670, light distributingelements 740 disposed on a major surface (e.g., a top major surface) ofwaveguide 680, and light distributing elements 750 disposed on a majorsurface (e.g., a top major surface) of waveguide 690. In some otherembodiments, the light distributing elements 730, 740, 750, may bedisposed on a bottom major surface of associated waveguides 670, 680,690, respectively. In some other embodiments, the light distributingelements 730, 740, 750, may be disposed on both top and bottom majorsurface of associated waveguides 670, 680, 690, respectively; or thelight distributing elements 730, 740, 750, may be disposed on differentones of the top and bottom major surfaces in different associatedwaveguides 670, 680, 690, respectively.

The waveguides 670, 680, 690 may be spaced apart and separated by, e.g.,gas, liquid, and/or solid layers of material. For example, asillustrated, layer 760 a may separate waveguides 670 and 680; and layer760 b may separate waveguides 680 and 690. In some embodiments, thelayers 760 a and 760 b are formed of low refractive index materials(that is, materials having a lower refractive index than the materialforming the immediately adjacent one of waveguides 670, 680, 690).Preferably, the refractive index of the material forming the layers 760a, 760 b is 0.05 or more, or 0.10 or less than the refractive index ofthe material forming the waveguides 670, 680, 690. Advantageously, thelower refractive index layers 760 a, 760 b may function as claddinglayers that facilitate total internal reflection (TIR) of light throughthe waveguides 670, 680, 690 (e.g., TIR between the top and bottom majorsurfaces of each waveguide). In some embodiments, the layers 760 a, 760b are formed of air. While not illustrated, it will be appreciated thatthe top and bottom of the illustrated set 660 of waveguides may includeimmediately neighboring cladding layers.

Preferably, for ease of manufacturing and other considerations, thematerial forming the waveguides 670, 680, 690 are similar or the same,and the material forming the layers 760 a, 760 b are similar or thesame. In some embodiments, the material forming the waveguides 670, 680,690 may be different between one or more waveguides, and/or the materialforming the layers 760 a, 760 b may be different, while still holding tothe various refractive index relationships noted above.

With continued reference to FIG. 9A, light rays 770, 780, 790 areincident on the set 660 of waveguides. It will be appreciated that thelight rays 770, 780, 790 may be injected into the waveguides 670, 680,690 by one or more image injection devices 360, 370, 380, 390, 400 (FIG.6).

In some embodiments, the light rays 770, 780, 790 have differentproperties, e.g., different wavelengths or different ranges ofwavelengths, which may correspond to different colors. The in-couplingoptical elements 700, 710, 720 each deflect the incident light such thatthe light propagates through a respective one of the waveguides 670,680, 690 by TIR. In some embodiments, the incoupling optical elements700, 710, 720 each selectively deflect one or more particularwavelengths of light, while transmitting other wavelengths to anunderlying waveguide and associated incoupling optical element.

For example, in-coupling optical element 700 may be configured todeflect ray 770, which has a first wavelength or range of wavelengths,while transmitting rays 1242 and 1244, which have different second andthird wavelengths or ranges of wavelengths, respectively. Thetransmitted ray 780 impinges on and is deflected by the in-couplingoptical element 710, which is configured to deflect light of a secondwavelength or range of wavelengths. The ray 790 is deflected by thein-coupling optical element 720, which is configured to selectivelydeflect light of third wavelength or range of wavelengths.

With continued reference to FIG. 9A, the deflected light rays 770, 780,790 are deflected so that they propagate through a correspondingwaveguide 670, 680, 690; that is, the in-coupling optical elements 700,710, 720 of each waveguide deflects light into that correspondingwaveguide 670, 680, 690 to in-couple light into that correspondingwaveguide. The light rays 770, 780, 790 are deflected at angles thatcause the light to propagate through the respective waveguide 670, 680,690 by TIR. The light rays 770, 780, 790 propagate through therespective waveguide 670, 680, 690 by TIR until impinging on thewaveguide's corresponding light distributing elements 730, 740, 750.

With reference now to FIG. 9B, a perspective view of an example of theplurality of stacked waveguides of FIG. 9A is illustrated. As notedabove, the in-coupled light rays 770, 780, 790, are deflected by thein-coupling optical elements 700, 710, 720, respectively, and thenpropagate by TIR within the waveguides 670, 680, 690, respectively. Thelight rays 770, 780, 790 then impinge on the light distributing elements730, 740, 750, respectively. The light distributing elements 730, 740,750 deflect the light rays 770, 780, 790 so that they propagate towardsthe out-coupling optical elements 800, 810, 820, respectively.

In some embodiments, the light distributing elements 730, 740, 750 areorthogonal pupil expanders (OPE's). In some embodiments, the OPE'sdeflect or distribute light to the out-coupling optical elements 800,810, 820 and, in some embodiments, may also increase the beam or spotsize of this light as it propagates to the out-coupling opticalelements. In some embodiments, the light distributing elements 730, 740,750 may be omitted and the in-coupling optical elements 700, 710, 720may be configured to deflect light directly to the out-coupling opticalelements 800, 810, 820. For example, with reference to FIG. 9A, thelight distributing elements 730, 740, 750 may be replaced without-coupling optical elements 800, 810, 820, respectively. In someembodiments, the out-coupling optical elements 800, 810, 820 are exitpupils (EP's) or exit pupil expanders (EPE's) that direct light in aviewer's eye 210 (FIG. 7). It will be appreciated that the OPE's may beconfigured to increase the dimensions of the eye box in at least oneaxis and the EPE's may be to increase the eye box in an axis crossing,e.g., orthogonal to, the axis of the OPEs. For example, each OPE may beconfigured to redirect a portion of the light striking the OPE to an EPEof the same waveguide, while allowing the remaining portion of the lightto continue to propagate down the waveguide. Upon impinging on the OPEagain, another portion of the remaining light is redirected to the EPE,and the remaining portion of that portion continues to propagate furtherdown the waveguide, and so on. Similarly, upon striking the EPE, aportion of the impinging light is directed out of the waveguide towardsthe user, and a remaining portion of that light continues to propagatethrough the waveguide until it strikes the EP again, at which timeanother portion of the impinging light is directed out of the waveguide,and so on. Consequently, a single beam of incoupled light may be“replicated” each time a portion of that light is redirected by an OPEor EPE, thereby forming a field of cloned beams of light, as shown inFIG. 6. In some embodiments, the OPE and/or EPE may be configured tomodify a size of the beams of light.

Accordingly, with reference to FIGS. 9A and 9B, in some embodiments, theset 660 of waveguides includes waveguides 670, 680, 690; in-couplingoptical elements 700, 710, 720; light distributing elements (e.g.,OPE's) 730, 740, 750; and out-coupling optical elements (e.g., EP's)800, 810, 820 for each component color. The waveguides 670, 680, 690 maybe stacked with an air gap/cladding layer between each one. Thein-coupling optical elements 700, 710, 720 redirect or deflect incidentlight (with different in-coupling optical elements receiving light ofdifferent wavelengths) into its waveguide. The light then propagates atan angle which will result in TIR within the respective waveguide 670,680, 690. In the example shown, light ray 770 (e.g., blue light) isdeflected by the first in-coupling optical element 700, and thencontinues to bounce down the waveguide, interacting with the lightdistributing element (e.g., OPE's) 730 and then the out-coupling opticalelement (e.g., EPs) 800, in a manner described earlier. The light rays780 and 790 (e.g., green and red light, respectively) will pass throughthe waveguide 670, with light ray 780 impinging on and being deflectedby in-coupling optical element 710. The light ray 780 then bounces downthe waveguide 680 via TIR, proceeding on to its light distributingelement (e.g., OPEs) 740 and then the out-coupling optical element(e.g., EP's) 810. Finally, light ray 790 (e.g., red light) passesthrough the waveguide 690 to impinge on the light in-coupling opticalelements 720 of the waveguide 690. The light in-coupling opticalelements 720 deflect the light ray 790 such that the light raypropagates to light distributing element (e.g., OPEs) 750 by TIR, andthen to the out-coupling optical element (e.g., EPs) 820 by TIR. Theout-coupling optical element 820 then finally out-couples the light ray790 to the viewer, who also receives the out-coupled light from theother waveguides 670, 680.

FIG. 9C illustrates a top-down plan view of an example of the pluralityof stacked waveguides of FIGS. 9A and 9B. As illustrated, the waveguides670, 680, 690, along with each waveguide's associated light distributingelement 730, 740, 750 and associated out-coupling optical element 800,810, 820, may be vertically aligned. However, as discussed herein, thein-coupling optical elements 700, 710, 720 are not vertically aligned;rather, the in-coupling optical elements are preferably non-overlapping(e.g., laterally spaced apart as seen in the top-down view). Asdiscussed further herein, this nonoverlapping spatial arrangementfacilitates the injection of light from different resources intodifferent waveguides on a one-to-one basis, thereby allowing a specificlight source to be uniquely coupled to a specific waveguide. In someembodiments, arrangements including nonoverlapping spatially-separatedin-coupling optical elements may be referred to as a shifted pupilsystem, and the in-coupling optical elements within these arrangementsmay correspond to sub pupils.

Metasurfaces and Optical Elements Based on Metasurfaces

Display systems may employ various optical elements for controlling thepropagation of light. However, in some contexts, such as display systemsincluding a head-mounted display device (e.g., the display system 80described supra with reference to FIG. 2), conventional optical elementsmay not be desirable or suitable, owing to their relatively heavyweight, large size, manufacturing challenges, and/or deficiencies inoptical properties such as diffraction angles and diffractionefficiency.

For example, as described above with reference to FIGS. 9A-9C, displaysystems according to various embodiments may include optical elements(e.g., incoupling optical elements, light distributing elements andoutcoupling optical elements), which may include diffraction gratings.Furthermore, as further described above with reference to FIGS. 9A-9C,light that is coupled into a corresponding waveguide preferablypropagates within the waveguide by total internal reflection (TIR). Toachieve TIR, it may be desirable for the diffraction grating to haverelatively high diffraction angles relative to a surface normal. Inaddition, high diffraction efficiencies are desirable to provide goodlight intensity and image brightness. However, diffraction gratingscapable of achieving high diffraction angles and high diffractionefficiencies for visible light remain a challenge. To address these andother needs, embodiments of optical elements disclosed herein, e.g.,diffraction gratings, utilize metasurfaces.

Metasurfaces may include surface structures that can locally modify thepolarization, phase and/or amplitude of light in reflection ortransmission. The metasurfaces may include an array ofsubwavelength-sized and/or subwavelength-spaced phase shift elementswhose patterns are configured to control the wavefront of light, suchthat various optical functionalities can be derived therefrom, includingbeam shaping, lensing, beam bending, and polarization splitting. Thefactors that can be used to manipulate the wavefront of the lightinclude the material, size, geometry and orientation of the surfacestructures. By arranging the surface structures with distinct scatteringproperties on a surface, space-variant metasurfaces can be generated,throughout which optical wavefronts can be substantially manipulated.

In conventional optical elements such as lenses and waveplates, thewavefront is controlled via propagation phases in a medium much thickerthan the wavelength. Unlike conventional optical elements, metasurfacesinstead induce phase changes in light using subwavelength-sizedresonators as phase shift elements. Because metasurfaces are formed offeatures that are relatively thin and uniform in thickness, they can bepatterned across a surface using thin film processing techniques such assemiconductor processing techniques, as well as direct-printingtechniques such as nanoimprint techniques. One example of replacing aconventional optical element with a metasurface is illustrated withreference to FIGS. 10A-10C. FIG. 10A schematically illustrates across-sectional view of a conventional optical element, e.g., a glassaxicon 1102. As illustrated, a typical conventional optical element suchas a glass axicon formed of, e.g. a glass lens, can be a few millimetersin thickness. In contrast, FIG. 10B schematically illustrates across-sectional view of an optical element, e.g., a metasurface axicon1104, which may be formed of a metal or semiconductor metasurface anddisposed on a substrate, e.g., a quartz substrate. Compared to theconventional axicon 1102, the metasurface axicon 1104 can be about tensto hundreds of nanometers thick, making them suitable for opticalsystems requiring compact optical elements, such as a head-mounteddisplay device. FIG. 10C illustrates the transmitted, nondiffractingBessel beam profile 1106 that results when the metasurface axicon 1104is illuminated with a collimated Gaussian left circularly polarized(LCP) light beam at a 550-nm wavelength. As illustrated, a desired beamprofile 1106 can be achieved using a metasurface axicon that can beorders of magnitude thinner compared to a conventional axicon. Similarresults can be obtained for various other optical elements, such asgratings.

Waveplates Based on Geometric Phase Metasurfaces

Without being bound to any theory, when a light beam is taken along aclosed cycle in the space of polarization states of light, it mayacquire a dynamic phase from the accumulated path lengths as well asfrom a geometric phase. The dynamic phase acquired from a geometricphase is due to local changes in polarization. Some optical elementsbased on a geometric phase to form a desired phase front may be referredto as Pancharatnam-Berry phase optical elements (PBOEs). PBOEs may beconstructed from wave plate elements for which the orientation of thefast axes depends on the spatial position of the waveplate elements.

Without be limited by theory, by forming a metasurface with half-waveplates formed of geometric phase optical elements, e.g., PBOEs, withtheir fast axes orientations according to a function θ(x,y), an incidentcircularly polarized light beam may be fully transformed to a beam ofopposite helicity having a geometric phase equal toϕ_(g)(x,y)=+/−2θ(x,y). By controlling the local orientation of the fastaxes of the wave plate elements between 0 and π, phasepickups/retardadations may be achieved that cover the full 0-to-2πrange, while maintaining relatively high and uniform transmissionamplitude across the entire optical element, thereby providing a desiredwavefront.

An example of a waveplate based on geometric phase, and the resultingphase pick-up/retardation and absorption, is illustrated with referenceto FIGS. 11A-11D. FIG. 11A illustrates an example waveplate 1100 formedof a metasurface comprising a plurality of nanobeams 1104, undertop-down illumination by incident light 1108 under a transverse electric(TE) polarization (with the electric field polarized normal to thelength of the structure) and an orthogonal transverse magnetic (TM)polarization. The thickness of the resonant structures may be smallcompared with the freespace wavelength of the incident light 1104. Inthe illustrated example, the nanobeams 1104 are 120 nm wide in thex-direction and 100 nm thick in the z-direction. In the illustratedexample, the nanobeams 1104 are formed of Si, which has been found tosupport a relatively strong resonance within the wavelength range ofinterest as described with reference to FIGS. 11B-11D.

FIG. 11B illustrates simulated phase wavefronts resulting from thewaveplate 1100 illustrated above with reference to FIG. 11A. Compared tothe finite element simulation 1112 of the incident wavefront, the finiteelement simulation 1116 shows that the wavefront of a TE-polarized lightbeam at 550 nm is delayed by 0.14π. The simulation 1120 of the wavefrontshows that the wavefront of a TM-polarized light is delayed evenfurther, by 1.15π. As a result, the phase retardation between the twoorthogonal polarizations is about π, and the beam array serves as a halfwaveplate.

FIG. 11C illustrates simulated spectra of phase retardation of aTM-polarized light with respect to a TE-polarized light beam resultingfrom a waveplate similar to that described above with reference to FIG.11A. By sweeping the wavelength from 490 to 700 nm, the phaseretardation of the wave plate varies from about 0.4π to 1.2π. Simulatedspectra 1128, 1132 and 1136 illustrate the phase retardation for blazedgratings comprising nanobeam arrays with beam widths of 100 nm, 120 nm,140 nm, respectively, for a nominal thickness of the nanobeams 1104 of100 nm. For comparison, the simulate spectrum 1140 shows a comparativelysmall phase retardation of 0.063π for a 100-nm thick film of calcite, anaturally birefringent crystal. The square symbols illustrateexperimental measurement for an array of 120-nm beams, showing goodagreement with the simulations. The inset shows an SEM image of anactually fabricated blaze grating 1100.

FIG. 11D illustrates simulated absorption spectra 1144 and 1148 of awaveplate comprising a nanobeam array with a beam width of 120 nm,corresponding to the phase retardation spectrum 1132 of FIG. 11C, underTM and TE illumination, respectively. Insets 1152 and 1156 illustratemagnetic field distribution |Hy| of TE illumination and electrical fielddistribution |Ey| of TM illumination at a wavelength of 600 nm,respectively.

Referring to FIGS. 11C and 11D, without being bound to any theory, thesubstantial swing in the phase retardation as illustrated, e.g., by thephase retardation spectrum 1132, may be attributed to a relativelystrong resonance under TE illumination, as indicated by the absorptionspectrum 1148 and a relatively weak second-order TM resonance, asindicated by the absorption spectrum 1144. The order of the resonance isdetermined by the number of field maxima inside the nanobeam (FIG. 11D,insets). As illustrated, the array's TE absorption resonance asillustrated by, e.g., absorption spectrum 1148, and the associated swingin the phase retardation as illustrated by, e.g., the phase retardationspectrum 1132, may be spectrally tuned in part by changing feature sizesof the nanobeams 1104, including the width.

In the following, with reference to FIGS. 12A-12H, a construction 1200of a geometric PB phase based on geometrically rotated waveplateelements is described. In particular, the PB phase configured as ahalf-wave plate with a phase retardation of π is described. The eighthalf-waveplate elements may be arranged as being equally spaced andfeature a constant orientation-angle difference Δθ between neighboringwaveplates. For illustrative purposes, the bottom row schematicallydepicts the rotation of the polarization vector of an incident lightbeam with left circular polarization, i.e. a |LCP> state. The middle rowillustrates half-wave plate elements constructed from nanobeam arrayssimilar to those described with reference to FIGS. 11A-11D, with theirfast axis oriented at different angles θ relative to the vertical axis.The top row schematically illustrates corresponding polarization vectorsof the light behind transmitted through the waveplate elements. Circularpolarizations and anti-clockwise orientation angles of fast axis ofwaveplate are defined from the point of view of the light source.

Still referring to FIGS. 12A-12H, the incident light beam may bedescribed by polarization vectors 1204 and 1208 having equal amplitudesin the x and y directions, respectively, and a phase delay 1212 of π/2between the polarization vectors. In operation, the half waveplate worksby shifting the phase between the two perpendicular polarizations by aphase of π. The net result of this action is to flip the electric fielddirected along the slow axis and to maintain the electric field alongthe fast axis. This action may also be viewed as one in which theoriginal polarization vector is flipped to its mirror image with thefast axis serving as the mirror. When considering a helical incidentstate in which a polarization vector that rotates in time, one may seethat the action of the waveplate is to switch helicity from |LCP> to|RCP>, or vice versa.

Referring to the bottom row of FIG. 12A, the electric field of anincident |LCP> beam is directed upward in the positive y axis at aninitial time t=t₀, as indicated by the vector 1204. A quarter of anoptical cycle later (i.e., π/2), the light is directed along thenegative y-direction, as represented by the vector 1208. The action ofthe waveplate in the middle row of FIG. 12A is to mirror the vectors1204 and 1208 in a mirror placed in the plane of the fast axis and thepropagation direction of the light. The action of this mirror is to flipthe vector 1204 to the positive x-direction and to keep the vector 1208in the original direction. As a result, the |LCP> beam is transformedinto a |RCP> beam.

FIGS. 12B-12H illustrate how the polarization vectors of an |LCP> beamchanges when the fast axes of the waveplates are rotated by an angle θof π/4, π/2, 3π/4, π, 5π/4, 3π/2 and 7π/4, respectively. Independent ofthe rotation angle, a |RCP> output beam is produced. However, theproduced phase delay of the vectors 1204 and 1208 with reference to FIG.12A is given by φ_(g)=2θ. For example, when θ=π/2 as shown in FIG. 12E,the action of the waveplate it to keep the vector 1204 in the samedirection while flipping the vector 1208 from the negative y-directioninto the positive y-direction. This produces a |RCP> beam that isdelayed by φ_(g)=2θ=π for incident light of LCP. As such, for theillustrated half waveplate, it will take half an optical cycle longerbefore the state shown in FIG. 12A is reached.

Thus, as an illustrative example, after passing through the eighthalf-waveplate elements that are equally spaced and feature a constantorientation-angle difference, e.g., Δθ=π/8 between neighbors, thetransmitted RCP waves display a constant phase difference Δφ_(g)=π/4between neighboring waveplates. By using eight waveplate elements withfast-axes orientation varying between 0 and π, phaseretardations/pickups may be achieved that covers the full 0-2π range.However, fabricating half-wave plate elements having a high diffractionangle for visible light may be challenging. This is because thediffraction angle depends, among other things, on the length of a periodof periodically repeating waveplate elements, and forming the relativelyhigh number of half-waveplate elements within a relatively small lengthof the period may be difficult due to spatial constraints. In thefollowing, embodiments of diffraction grating in which phaseretardations/pickups may be achieved that covers the full 0-2π range atrelatively high diffraction angles and diffraction efficiencies, as wellas uniformity of diffraction efficiencies across a relatively wide angleof incidence.

Diffraction Gratings Based on Geometric Phase Metasurfaces

Applications of the metasurfaces comprising PBOEs include diffractiongratings, e.g., blazed gratings, focusing lenses, and axicons, amongvarious other applications. As described herein, a blazed grating iscapable of steering a light beam into several diffracted orders. Theblazed grating may be configured to achieve high grating efficiency inone or more diffraction orders, e.g., +1 and/or −1 diffraction orders,thus resulting in the optical power being concentrated in the desireddiffraction order(s) while the residual power in the other orders (e.g.,the zeroth) is low. In the present disclosure, various embodiments ofmetasurfaces comprising PBOEs configured as diffraction gratings aredescribed. The diffraction gratings according to various embodimentshave a combination of desirable optical properties, including one ormore of high diffraction angle, high diffraction efficiency, a widerange of acceptance angle and a highly uniform diffraction efficiencywithin the range of acceptance angle. These desirable optical propertiesmay result from a combination of various inventive aspects, includingthe material, dimensions and geometric configurations of the elements ofthe metasurfaces.

As described herein, visible light may include light having one or morewavelengths in various color ranges, including red, green, or blue colorranges. As described herein, red light may include light of one or morewavelengths in the range of about 620-780 nm, green light may includelight of one or more wavelengths in the range of about 492-577 nm, andblue light may include light of one or more wavelengths in the range ofabout 435-493 nm. Thus, visible may include light of one or morewavelengths in the range of about 435 nm-780 nm.

As described herein, features, e.g., as nanobeams, lines, line segmentsor unit cells, that are parallel, nominally parallel or substantiallyparallel, refer to features having elongation directions that differ byless than about 10%, less than about 5% or less than about 3% in theelongation directions. In addition, features that are perpendicular,nominally perpendicular or substantially perpendicular refer to featureshaving elongation directions that deviate from 90 degrees in theelongation directions by less than about 10%, less than about 5% or lessthan about 3%.

As described herein, structures configured to diffract light, such asdiffraction gratings, may diffract light in a transmission mode and/orreflection mode. As described herein, structures that are configured todiffract light in transmission mode refer to structures in which theintensity of diffracted light on the opposite side of the structures asthe light-incident side is greater, e.g., at least 10% greater, 20%greater or 30% greater, compared to the intensity of diffracted light onthe same side of the structures as the light-incident side. Conversely,structures that are configured to diffract light in reflection moderefer to structures in which the intensity of diffracted light on thesame side of the structures as the light-incident side is greater, e.g.,at least 10% greater, 20% greater or 30% greater, compared to theintensity of diffracted light on the opposite side of the structures asthe light-incident side.

As described herein, a line, also referred to as a beam or nanobeam, isan elongated structure having a volume. It will be appreciated that thelines are not limited to any particular cross-sectional shape. In someembodiments, the cross-sectional shape is rectangular.

FIGS. 13A and 13B illustrate a cross-sectional side view and a top-downview, respectively, of a diffraction grating 1300 comprising ametasurface having geometric phase optical elements, according to someembodiments. The diffraction grating 1300 comprises a 2-level geometricphase metasurface. The cross-sectional side view illustrated withreference to FIG. 13A is that of a cross-section AA′ illustrated in FIG.13B. The diffraction grating 1300 includes a substrate 1304 having asurface on which a metasurface 1308 configured to diffract light havinga wavelength in the visible spectrum is formed. The metasurface 1308includes one or more first lines or nanobeams 1312 having a firstorientation and extending generally in a first lateral direction (e.g.,the y-direction) and a plurality of second lines or nanobeams 1316having a second orientation extending generally in a second direction(e.g., the x-direction). The first lines or nanobeams 1312 may beconsidered to form a first set of nanobeams and the second lines ornanobeams 1316 may be considered to form a second set of nanobeams. Theone or more first lines 1312 and the second lines 1316 are disposedadjacent to one another in the second direction, and the first lines1312 and the second lines 1316 alternatingly repeat in the seconddirection at a period less than the wavelength of light which themetasurface is configured to diffract.

Preferably, the first lines 1312 each have the same width. In someembodiments, the second lines 1316 are laterally stacked in they-direction between adjacent pairs of the one or more first lines 1312.Without be limited by theory, the one or more first lines 1312 and thesecond lines 1316 are oriented at an angle relative to each other topreferably cause a phase difference between the visible light diffractedby the one or more first lines 1312 and the visible light diffracted bythe second lines 1316, where the phase difference between the visiblelight diffracted by the one or more first lines 1312 and the visiblelight diffracted by the second lines 1316 is twice the angle.

In some embodiments, similar to the combination of wave platesillustrated above with reference to FIGS. 12A-12H, the phase differencecaused by the relative orientations of one or more first lines 1312relative to the second lines 1316, which may vary between 0 and π, phasepickups/retardations may be achieved that covers the full 0-2π range. Insome embodiments, when the one of the one or more first lines 1312 andthe second lines 1316 are rotated by π relative to the other, e.g.,perpendicular to each other, a phase pickup/retardation of 2π may beachieved between the one or more first lines 1312 and the second lines1316. That is, unlike FIGS. 12A-12H, phase pickups/retardations coveringthe full 0-2π range may be achieved based on the 2-level geometric phasemetasurface having lines oriented in just two different directions,according to some embodiments. Advantageously, unlike FIGS. 12A-12H, thecombination of wave plates illustrated with reference to FIGS. 12A-12H,the foot print occupied by the illustrated metasurface 1308 is morecompact, and has a period less than or equal to a wavelength in thevisible spectrum, which in turn enables a relatively high diffractionangle θ of the diffracted beams 1338, 1342.

The first lines 1312 and the second lines 1316 are formed of anoptically transmissive material. As described herein and throughout thespecification, a “transmissive” or “transparent” structure, e.g., atransmissive substrate, may allow at least some, e.g., at least 20, 30,50, 70 or 90%, of an incident light, to pass therethrough. Accordingly,a transparent substrate may be a glass, sapphire or a polymericsubstrate in some embodiments. A “reflective” structure, e.g., areflective substrate, may reflect at least some, e.g., at least 20, 30,50, 70, 90% or more of the incident light, to reflect therefrom.

The one or more first lines 1312 and the second lines 1316 may bedescribed as being protrusions, ridges creases or nanowires thatprotrude out of the page, extend along the page, and having a width.Additionally or alternatively, regions of separation between adjacentfirst lines 1312 and/or between adjacent second lines 1316 may bedescribed as being depressions, troughs, recesses or trenches thatrecess into the page and having a spacing. In some embodiments, thefirst lines 1312 and the second lines 1316 are elongated rectangularstructures having a substantially rectangular cross-sectional shape inthe y-z plane. However, other embodiments are possible, where the firstlines 1312 and the second lines 1316 have cross sectional shape may takeon a shape of a circle, an ellipse, a triangle, a parallelogram, arhombus, a trapezoid, a pentagon or any suitable shape.

In the following, various configurations including dimensions andgeometric arrangements of the one or more first lines 1312 and thesecond lines 1316 are described, whose combined effect is to produce thegrating based on geometric phase optical elements with desirable opticalproperties described herein, including one or more of a relatively highdiffraction angle, a relatively high diffraction efficiency, arelatively wide range of acceptance angle and a relatively uniformefficiency within the range of acceptance angle.

Still referring to FIGS. 13A and 13B, in operation, when an incidentlight beam 1330, e.g., visible light, is incident on the metasurface1308 at an angle of incidence α measured relative to a plane normal tothe surface 1304S and extending in a direction parallel to the firstlines 1312, e.g., the y-z plane, the grating 1300 partially transmitsthe incident light as a transmitted light beam 1334 and partiallydiffracts the incident light as a diffracted light beam of +1 order 1342at a diffraction angle θ₁ and a diffracted light beam of −1 order 1338at a diffraction angle θ₂, where the diffraction angles are measuredrelative to the same plane for measuring α, e.g., the y-z plan. When oneor both of the diffracted light beams 1338 and 1342 are diffracted at adiffraction angle that exceeds a critical angle θ_(TIR) for occurrenceof total internal reflection in the substrate 1304 configured as awaveguide, the diffracted light beams 1338 and 1342 propagate in theirrespective opposite directions along the x-axis under total internalreflection (TIR) until the light beams reach the OPE's/EPE's 1346, whichmay correspond to the light distributing elements 730, 740, 750 and theout-coupling optical elements 800, 810, 820 (FIG. 9B).

According to various embodiments, the one or more first lines 1312 andthe second lines 1316 are formed of a material that provides low Ohmicloss of photons, such that the diffraction efficiency is at a highlevel. Without being bound to any theory, among other things, Ohmic lossof photons may depend on whether the first lines 1312 and/or the secondlines 1316 are formed of a material that is metallic versussemiconducting or insulating. As described herein, whether a material ismetallic, semiconducting or insulating may depend on the electronicenergy band structure of the material in energy-wave vector space, orE-k space. An electronic energy band structure may be described ashaving a highest occupied molecular orbital (HOMO), which may also bereferred to as a valence band, and a lowest unoccupied molecular orbital(LUMO), which may also be referred to as a conduction band. An insulatorhas a difference in energy between a HOMO and a LUMO that substantiallyexceeds the energy corresponding to a wavelength range the metasurfaceis configured to diffract. A semiconductor has a difference in energybetween a HOMO and a LUMO that is substantially comparable to the energycorresponding to the wavelength range the metasurface is configured todiffract. As described herein, a metal has a difference in energybetween a HOMO and a LUMO that is zero or negative. As a result, metalshave a substantial concentration of free or delocalized electrons. Thefree or delocalized electrons may collectively interact with light togenerate plasmons, which refers to quasiparticles arising quantizationof plasma oscillation of free electrons. When at least one of thedimensions, e.g., the width of the first lines 1312 and the second lines1316, are sufficiently small, e.g., less than the wavelength of incidentlight, plasmons may become confined to surfaces and interact stronglywith light, resulting in surface plasmons. Under some circumstances,when the frequency of incident photons matches the natural frequency ofsurface electrons oscillating against the restoring force of positivenuclei, surface plasmon resonance (SPR) may occur, resulting in resonantoscillation of conduction electrons.

Without being bound to any theory, when the one or more first lines 1312and/or the second lines 1316 are formed of a metal, the Ohmic loss ofphotons may at least partially be caused by plasmon resonance, which mayoccur at or near SPR wavelengths. Accordingly, in some embodiments, eachof the one or more first lines 1312 and the second lines 1316 are formedof a nonmetallic material, e.g., a semiconductor or an insulator, inwhich the concentration of free electrons are, e.g., less than about1×10¹⁹/cm³, less than about 1×10¹⁸/cm³, less than about 1×10¹⁷/cm³, orless than about 1×10¹⁶/cm³, according to some embodiments. However,embodiments are not so limited and, in some embodiments, one or both ofthe first lines 1312 and the second lines 1316 may be formed of metals.

Still referring to FIGS. 13A, 13B, the inventors have found that, insome embodiments, it may be advantageous to form the first lines 1312and the second lines 1316 using a semiconductor or an insulator, whichmay provide low levels of Ohmic loss arising from plasmon generation andcorrespondingly increased diffraction efficiency. The resulting firstlines 1312 and the second lines 1316 imposes a polarization-dependentphase shift on the transmitted light and modifies both its phase andpolarization. Without being bound to any theory, when formed of asemiconductor or an insulator, each of the one or more first lines 1312and the second lines 1316 may be considered as a waveguide operating asa Fabry-Pérot resonator having an effective refractive index andimposing a polarization-dependent phase shift on the transmitted light.To reduce the Ohmic loss arising from plasmon generation and to increasethe diffraction efficiency, the one or more first lines 1312 and thesecond lines 1316 are formed of a material having certain materialproperties, including relatively low free electron concentration,relatively high bulk refractive index, as discussed herein.

As discussed above, to provide a high diffraction efficiency, inaddition to realizing other advantages, it may be desirable to have thefirst lines 1312 and/or the second lines 1316 be formed of a materialhaving a relatively lower concentration of free electrons. Accordingly,when formed of a semiconductor or an insulator, under variousembodiments, each of the first lines 1312 and the second lines 1316 arenot intentionally doped with free-electron generating dopants or, whenintentionally doped, they are doped with a dopant, e.g., an n-typedopant, at a concentration less than less than about 1×10¹⁹/cm³, lessthan about 1×10¹⁸/cm³, less than about 1×10¹⁷/cm³, or less than about1×10¹⁶/cm³, according to various embodiments. Without being bound to anytheory, the relatively low dopant concentration may be advantageous,e.g., in reducing the Ohmic loss arising from plasmon generation and/orsurface plasmon resonance, among other advantages.

Without being bound to any theory, when the first lines 1312 and/or thesecond lines 1316 are formed of a semiconductor or an insulator, whilethe Ohmic loss arising from plasmonic absorption may be reduced, someOhmic loss is still believed to occur from optical absorption arisingfrom photon-absorbing electronic transitions, including elastic andinelastic electronic transitions. For example, optical absorption mayoccur when a photon having energy greater than a band bap between theHOMO and the LUMO of the semiconductor or the insulator is absorbed,resulting in generation of electron-hole pairs. Accordingly, it may beadvantageous to reduce optical absorption arising from photo-absorbingelectronic transitions. Accordingly, in some embodiments, the firstlines 1312 and/or the second lines 1316 may be formed of a materialwhose absorption coefficient value is less than about 5×10⁵/cm, lessthan about 1×10⁵/cm, less than 5×10⁴/cm or less than 1×10⁴/cm, less thanabout 5×10³/cm, less than about 1×10³/cm, less than about 5×10²/cm, orformed of a material whose absorption coefficient value is within arange defined by any of the above values, for an incident light having awavelength in the visible spectrum.

Without being bound to any theory, when the first lines 1312 and thesecond lines 1316 having subwavelength feature sizes support leaky moderesonances they may confine light, thereby causing phase retardation inthe scattered light waves produced under TE and TM illumination. It hasbeen found that the effectiveness of confinement of light in the one ormore first lines 1312 and the second lines 1316 may arise from beingconfigured as waveguides operating as resonators, and the resultingdiffraction efficiency may depend on, among other factors, therefractive index of the material and subwavelength dimensions of thefirst lines 1312 and the second lines 1316.

Accordingly, in some embodiments, it may be desirable to have the firstlines 1312 and/or the second lines 1316 formed of a material having abulk refractive index (n_(1 bulk)) having a value higher than 2.0,higher than 2.5, higher than 3.0, higher than 3.3, higher than 3.5, or avalue that is in a range between any of these values. In someembodiments, the n_(1 bulk) is measured at a wavelength, e.g., a visiblewavelength, that the diffraction grating 1300 is configured to diffract.

The relatively high refractive index, among other advantages, may beachieved by forming the first lines 1312 and/or the second lines 1316using certain semiconductor materials. In some embodiments, when formedof a semiconductor material, the first lines 1312 and/or the secondlines 1316 may be formed of an elemental Group IV material (e.g., Si,Ge, C or Sn) or an alloy formed of Group IV materials (e.g., SiGe,SiGeC, SiC, SiSn, SiSnC, GeSn, etc.); Group III-V compound semiconductormaterials (e.g., GaP, GaAs, GaN, InAs, etc.) or an alloy formed of GroupIII-V materials; Group II-VI semiconductor materials (CdSe, CdS, ZnSe,etc.) or an alloy formed of Group II-VI materials. Each of thesematerials may be crystalline, polycrystalline or amorphous.

In some embodiments, the first lines 1312 and/or the second lines 1316are formed of silicon, e.g., silicon, amorphous silicon orpolycrystalline silicon. When formed of silicon, it may be more readilyfabricated or integrated using silicon-processing technologies.

The relatively high refractive index, among other advantages, may alsobe achieved by forming the first lines 1312 and/or the second lines 1316using certain insulators. When formed of an insulator, the one or morefirst lines 1312 and/or the second lines 1316 may be formed an oxidewhich includes a transition metal, e.g., titanium, tantalum, hafnium,zirconium, etc., according to some embodiments, including theirstoichiometric and substoichiometric forms. Examples of such oxidesinclude e.g., titanium oxide, zirconium oxide, and zinc oxide.

The first lines 1312 and/or the second lines 1316 may also be formed ofan oxide, a nitride or an oxynitride of a Group IV element, e.g.,silicon, according to some other embodiments, including theirstoichiometric and sub stoichiometric forms. Examples of such aninsulator includes, e.g., silicon oxide (SiO_(x)), silicon nitride(SiN_(x)) and silicon oxynitride (SiO_(x)N_(y)).

In some embodiments, the first lines 1312 and the second lines 1316 maybe formed of the same semiconductor or insulator material, which may beadvantageous for simplifying fabrication of the metasurface 1308.However, various embodiments are not so limited, and in someembodiments, the first lines 1312 and the second lines 1316 may beformed of different semiconductor or insulating materials.

With continued reference to FIGS. 13A and 13B, in addition to beingformed of various materials described above, the one or more first lines1312 and the second lines 1316 have particular combination of dimensionsto serve as subwavelength-sized resonators that induce phase shifts inlight.

In various embodiments, each of W_(nano1) of the first lines 1312 andW_(nano2) of the second lines 1316 is smaller than the wavelength oflight the metasurface 1308 is configured to diffract, and is preferablysmaller than a wavelength in the visible spectrum. In some embodiments,each of W_(nano1) and W_(nano2) is in the range of 10 nm to 1 μm, 10 nmto 500 nm, 10 nm to 300 nm, 10 nm to 100 nm or 10 nm to 50 nm, forinstance 30 nm. According to some embodiments, each of the one or morefirst lines 1312 has the same width W_(nano1). According to someembodiments, each of the second lines 1316 has the same width W_(nano2).According to some embodiments, the one or more first lines 1312 and thesecond lines 1316 have the same width, i.e., W_(nano1)=W_(nano2).However, in some other embodiments, W_(nano1) and W_(nano2) may besubstantially different. Furthermore, in some embodiments, differentones of the one or more first lines 1312 and/different ones of thesecond lines 1316 may have different widths.

According to some embodiments, immediately adjacent ones of the one ormore first lines 1312 in the second direction are separated by aconstant spacing s₁. In addition, one of the one or more first lines1312 and one of the second lines 1316 that are immediately adjacent toone another in the second direction are separated by a constant spacing52. According to some embodiments, one or both of s₁ and s₂ are smallerthan the wavelength the metasurface 1308 is configured to diffract. Inaddition, the first lines 1312 and the second lines 1316 have heightsh_(nano1) and h_(nano2), respectively. A particular combination of thespacings s₁, s₂ and the heights h_(nano1) and h_(nano2) may be chosensuch that a desired range (Δα) of angle of incidence α, sometimesreferred to as a range of angle of acceptance or a field-of-view (FOV),is obtained. As described herein. the desired range Δα may be describedby a range of angles spanning negative and positive values of α, outsideof which the diffraction efficiency falls off by more than 10%, 25%,more than 50%, or more than 75%, relative to the diffraction efficiencyat α=0. Having the Δα within which the diffraction efficiency isrelatively flat may be desirable, e.g., where uniform intensity ofdiffracted light is desired within the Δα. Referring back to FIG. 13A,the incident light beam 1330 is incident on the metasurface 1308 andsurface of the waveguide 1304 at an angle α relative to a surfacenormal, e.g., the y-z plane. According to some embodiments, as describedabove, the Δα is associated with the angular bandwidth for themetasurface 1308, such that the light beam 1330 within the Δα isefficiently diffracted by the metasurface 1308 at a diffraction angle θwith respect to a surface normal (e.g., the y-z plane). In particular,when θ is or exceeds θ_(TIR), the diffracted light propagates within thesubstrate 1304 under total internal reflection (TIR).

It has been found that Δα may depend on a shadowing effect created byadjacent ones of one or more first lines 1312 in the second directionand immediately adjacent ones of the second lines 1316 in the firstdirection. That is, when the incident light beam 1330 is incident at anangle of incidence α that is greater than a certain value, the incidentlight beam directed towards a feature may be blocked by an immediatelyadjacent feature. For example, the Δα may be associated with thearctangent of s₁/h_(nano1), s₂/h_(nano1) and/or s₂/h_(nano1). In variousembodiments, the ratios s₁/h_(nano1), s₂/h_(nano1) and/or s₂/h_(nano1)are selected such that Δα exceeds 20 degrees (e.g, +/−10 degrees), 30degrees (e.g., +/−15 degrees), 40 degrees (e.g., +/−20 degrees) or 50degrees (e.g., +/−25 degrees), or is within a range of angles defined byany of these values. The desired ratios s₁/h_(nano1), s₂/h_(nano1)and/or s₂/h_(nano1) may be realized where, e.g., each of s₁ and s₂ is inthe range of 10 nm to 1 μm, 10 nm to 300 nm, 10 nm to 100 nm or 10 nm to50 nm, for instance 30 nm. Of course, relatively lower values of s₁ ands₂ may be realized by where h_(nano1) and h_(nano2) have correspondinglyrelatively lower values.

Advantageously, the relatively high refractive index (n₁) of thematerial of the one or more first lines 1312 and/or the second lines1316 according to some embodiments allow for a relatively smallthickness or height. Accordingly, in various embodiments, the firstlines 1312 and the second lines 1316 have h_(nano1) and h_(nano2), whichmay be in the range of 10 nm to 1 μm, 10 nm to 500 nm, 10 nm to 300 nm,10 nm to 100 nm and 10 nm to 50 nm, for instance 107 nm, according tosome embodiments, depending on the n₁. For example, the h_(nano1) andh_(nano2) may be 10 nm to 450 nm where n₁ is more than 3.3, and 10 nm to1 μm where n₁ is 3.3 or less. As another example, the height the firstlines 1312 and the second lines 1316 may be 10 nm to 450 nm where thenanobeams are formed of silicon (e.g., amorphous or polysilicon).

According to various embodiments, the combination of s₁ and W_(nano1)may be selected such that a pitch (p_(nano1)) of the one or more firstlines 1312, defined as a sum of Si and W_(nano1), has a value obtainedby a sum of W_(nano1) selected from ranges of 10 nm to 1 μm, 10 nm to500 nm, 10 nm to 300 nm, 10 nm to 100 nm or 10 nm to 50 nm, and s₁selected from ranges of 10 nm to 1 μm, 10 nm to 300 nm, 10 nm to 100 nmor 10 nm to 50 nm, for instance p_(nano1)=95.5 nm.

Of course, relatively small values of s₁ and s₂ may be realized andh_(nano1) and h_(nano2) have correspondingly relatively small values.Advantageously, using a material with relatively high refractive indexn₁ to form the one or more first lines 1312 and/or the second lines1316, relatively small values of s₁, s₂, h_(nano1) and h_(nano2) may beobtained. This is because, as the inventors have found, the h_(nano1)and h_(nano2) may be inversely proportional to the bulk refractive indexof the material forming the first lines 1312 and the second lines 1316.Accordingly, for a material having bulk refractive index of 2.0-2.5,2.5-3.0, 3.0-3.5 and higher than 3.5, the h_(nano1) and h_(nano2) may bein the range of 500 nm to 1 μm, 300 nm to 500 nm, 100 nm to 300 nm and10 nm to 100 nm, respectively, in various embodiments. Thus, by theparticular combination of a material having a high bulk refractive indexn₁ of the one or more first lines 1312 and the second lines 1316 and thecorresponding dimensions s₁, s₂, h_(nano1) and h_(nano2), the overallpitch Λ_(a) may also be correspondingly decreased, which in turnincreases the diffraction angle θ, as described further below.

Preferably, the h_(nano1) and h_(nano2) are substantially equal, whichmay be advantageous for fabrication. However, embodiments are not solimited and the h_(nano1) and h_(nano2) may be substantially different.

In various embodiments, the first lines 1312 and/or the second lines1316 are formed of a material whose bulk refractive index (n_(1 bulk))is higher than the refractive index n₂ of the substrate 1304; i.e.,n_(1 bulk)>n₂. In some embodiments, the substrate 1304 may be configuredas a waveguide, and may correspond to the waveguides 310, 300, 290, 280,270 (FIG. 6) and/or waveguides 670, 680, and 690 (FIG. 9A). In suchapplications, the substrate preferably has a refractive index that isbetween that of air but less than n_(1 bulk), e.g., 1.5, 1.6, 1.7, 1.8,1.9, or higher but less than n_(1 bulk), which may provide benefits forincreasing the Δα of a display that forms an image by outputting lightfrom that substrate 1316. Examples of materials for forming thesubstrate 1304 include silica glass (e.g., doped silica glass), siliconoxynitride, transition metal oxides (e.g., hafnium oxide, tantalumoxide, zirconium oxide, niobium oxide, lithium niobate, aluminum oxide(e.g., sapphire)), plastic, a polymer, or other optically transmissivematerial having, e.g., a suitable refractive index as described herein.

Without being bound to any theory, when the one or more first lines 1312and/or the second lines 1316 have subwavelength dimensions as describedabove, the refractive indices of the first lines 1312 and/or the secondlines 1316 a may deviate from their bulk refractive index value, i.e.,n_(1 bulk). For instance, for a fundamental mode of resonance, the firstlines 1312 and/or the second lines 1316 may have an effective index ofrefraction, n_(1 eff), which may vary from about 1 (when the light ismostly in air) to about n_(1 bulk) (when the light is mostly in thelines and/or segments). Thus, in some embodiments, it is desirable tosatisfy the condition that n_(1eff)>n₂ by a sufficient value.Accordingly, in some embodiments, the materials for the first lines 1312and/or the second lines 1316 and for the substrate 1304 are selectedsuch that a difference (n_(1 bulk)-n₂) between the bulk refractive indexn_(1 bulk) of the material of the first lines 1312 and/or the secondlines 1316, and the refractive index n₂ of the substrate 1304, issufficiently large, e.g., 0.5 or higher, 1.0 or higher, 1.5 or higher,2.0 or higher, 2.5 or higher, or 3.0 or higher.

Still referring to FIGS. 13A and 13B, the metasurface 1308 may bedescribed as forming a plurality of metasurface unit cells 1320 thatrepeat at least in the x-direction. As described herein, a metasurfaceunit cell 1320 may be defined as a footprint having the smallestrepeating dimension in the x-direction, which includes the one or morefirst lines 1312 the second lines 1316. As a example, each unit cell1320 spans a unit cell width 1320 a measured from the left vertical sideof the left one of the first lines 1312 of one unit cell 1320 to theleft vertical side of the left vertical side of the left one of thefirst lines 1312 of an immediately adjacent unit cell 1320, and therebyincludes a pair of first lines 1312 and a column of second lines 1316stacked in the y-direction in the illustrated embodiments.

As described herein, the lateral dimension of the metasurface unit cells1320, or the period of repeating units of the unit cells 1320, may bereferred to herein as a unit cell pitch Λ_(a). The pitch Λ_(a) repeatsat least twice at regular intervals across the waveguide 1304 in thex-direction. In other words, the unit cell pitch Λ_(a) may be thedistance between identical points of directly neighboring unit cells1320. In various embodiments, the Λ_(a) may be smaller than thewavelength the grating 1300 is configured to diffract, and may besmaller than a wavelength, or any wavelength, in the range of about 435nm-780 nm. In some embodiments configured to diffract at least redlight, the Λ_(a) may be less than a wavelength (or any wavelength) inthe range of about 620-780 nm. In some other embodiments configured todiffract at least green light, the Λ_(a) may be less than a wavelength(or any wavelength) in the range of about 492-577 nm. In some otherembodiments configured to diffract at least blue light, the Λ_(a) may beless than a wavelength (or any wavelength) in the range of about 435-493nm. Alternatively, according to various embodiments, the Λ_(a) may be inthe range of 10 nm to 1 μm, including 10 nm to 500 nm or 300 nm to 500nm. It will be appreciated that each of the metasurfaces disclosedherein may be utilized to diffract light and may be part of the displaysystem 250 (FIG. 6) and that the display system 1000 may be configuredto direct light to the metasurface having a narrow band of wavelengths.Preferably, the Λ_(a) for a given metasurface is less than the smallestwavelength of the band of wavelengths that a light source of the displaysystem is configured to direct to the metasurface.

It has been found that, in some embodiments, the Λ_(a) may have a valuethat is less than a ratio mλ/(sin α+n₂ sin θ), where m is an integer(e.g., 1, 2, 3 . . . ) and α, n₂ and θ each have values describedelsewhere in the specification. For example, α may be within the rangeΔα exceeding 40 degrees, n₂ may be in the range of 1-2, and θ may be inthe range of 40-80 degrees.

In some embodiments, the Λ_(a) may be substantially constant across thesurface 1304S of the grating 1300 formed by a plurality of unit cells.However, embodiments are not so limited and in some other embodiments,Λ_(a) may vary across the surface 1304S.

Still referring to FIG. 13B, in some embodiments, each of the secondlines 1316 is shorter length than each of the one or more first lines1312 by at least a factor of two, three, four or more. However,embodiments in which the second lines 1316 are longer than the one ormore first lines 1312 are possible. According to various embodiments,the one or more first lines 1312 may have a length L₁ in the range of200 μm-5 mm nm, 200 μm-1 mm or 1 mm-5 mm. According to variousembodiments, the second lines 1316 may have a length L₂ in the range of100 nm-500 nm, 100 nm-300 nm and 300 nm-500 nm. In some embodiments, theone or more first lines 1312 may have a length L₁ corresponding to atotal lateral dimension of the optical element formed by themetasurface, e.g., corresponding to a length of an incoupling oroutcoupling optical element formed by the metasurface comprising thelines 1312. In some embodiments, the second lines have a length L₂ thatis about 40% to about 60% of a unit cell pitch Λ_(a), for instance about50% of Λ_(a). In some embodiments, L₁ is such that the one or more firstlines 1312 span a distance in the y-direction corresponding to fivesecond lines 1316. However, it will be understood that the one or morefirst lines 1312 may span a distance in the y-direction corresponding toany suitable number of second lines 1316 greater than one, e.g., greaterthan 10, greater than 20, greater than 50 or greater than 100, or in arange between any of 10, 20 and 100, according to various embodiments.

Still referring to FIGS. 13A and 13B, in some embodiments, each of thesecond lines 1316 have the same length such that the second lines 1316extend in the x-direction and coterminate without crossing any of theone or more first lines 1312. However, embodiments in which the secondlines 1316 have different lengths are possible.

Still referring to the illustrated embodiment of FIG. 13A, the directionof extension (y-direction) of the one or more first lines 1312 issubstantially perpendicular to the direction of extension (x-direction)of the second lines 1316. That is, the second lines 1316 are rotatedrelative to the one or more first lines 1312 by and angle of rotation ofπ/2 when viewed a direction of propagation of an incident light (i.e.,into the page). However, embodiments are not so limited, and the secondlines 1316 may extend in any direction that is rotated in acounterclockwise direction by an angle smaller than π/2 when viewed adirection of propagation of an incident light (i.e., into the page). Forexample, the second lines 1316 may be rotated relative the one or morefirst lines 1312 in a similar manner that the nanobeams of wave platesillustrated in FIGS. 12B-12H are rotated relative to the waveplateillustrated in FIG. 12A. For example, the second lines 1316 may berotated by relative to the one or more first lines 1312 by an angle ofrotation θ of π/4, π/2, 37π/4, π, 57π/4, 3π/2 and 7π/4, respectively.Thus, when an |LCP> beam is incident on the metasurface 1308 having thefirst and second lines 1312 and 1316, a |RCP> output beam is produced,where the resulting phase delay of the polarization vectorscorresponding to TE and TM polarizations may have a value of φ_(g)=2θ,where θ is the angle of rotation changes when the fast axes of thewaveplates are rotated by an angle of rotation θ. In particular, for theillustrated embodiment, the second lines 1316 that rotated by θ=π/2relative to the one or more first lines 1312 diffracts an incident lightbeam, e.g., an |LCP> beam, whereby a diffracted |RCP> beam is generated,where the diffracted beam is delayed by φ_(g)=2θ=π by the second lines1316. Thus, as the illustrated embodiment, after passing through themetasurface 1308 in which the alternating one or more first lines 1312and the second lines 1316 in the x-direction have a constantorientation-angle difference of Δθ=π/2, the transmitted RCP wavesdisplay a constant phase difference Δφ_(g)=π between adjacent ones ofthe one or more first lines 1312 and the second lines 1316. As a result,by having the fast-axes orientation vary between 0 and π, phasepickups/retardations that covers the full 0-2π range may be achieved,but with a much more compact unit cell pitch and higher diffractionangles compared to the illustrated example in FIGS. 12A-12H.

Display Devices Having Geometric Phase Metasurface-Based Gratings

As disclosed herein, in various embodiments described above, themetasurface 1308 may be implemented as an incoupling optical element(e.g., as one or more of the incoupling optical elements 700, 710, 720(FIG. 9A)) to incouple incident light such that the light propagatesthrough the substrate 1304 via total internal reflection. However, inrecognition that the metasurface 1308 may also be configured to deflectlight impinging on it from within the substrate 1304, in someembodiments, the metasurfaces disclosed herein may be applied to formoutcoupling optical elements, such as one or more of the outcouplingoptical elements 570, 580, 590, 600, 610 (FIG. 6) or 800, 810, 820 (FIG.9B) instead of, or in addition to, forming an incoupling optical elementat different locations on the surface 2000 a. In some other embodiments,the metasurface 1308 may be utilized as light distributing elements(e.g., OPE's) 730, 740, 750 (FIG. 9B). Where different waveguides havedifferent associated component colors, it will be appreciated that theoutcoupling optical elements and/or the incoupling optical elementsassociated with each waveguide may have a geometric size and/orperiodicity specific for the wavelengths or colors of light that thewaveguide is configured to propagate. Thus, different waveguides mayhave metasurfaces with different arrangements of the one or more firstlines 1312 and the second lines 1316. In particular, the differentarrangements may depend on the wavelength or the color of the incidentlight beam. For example, depending on the color of the incident lightbeam, the Λ_(a) may be configured differently according to thewavelength the grating 1300 is configured to diffract. For example, fordiffracting at least red light, green light or blue light, themetasurface 1308 may be configured to have a Λ_(a) that is less thanwavelengths in the range of about 620-780 nm, less than wavelengths inthe range of about 492-577 nm, and less than wavelengths in the range ofabout 435-493 nm, respectively. To scale the Λ_(a), parameters such asrefractive indices, widths, heights and spacings of the one or morefirst lines 1312 and/or the second lines 1316 may be adjustedproportionally. Alternatively, Λ_(a) may be kept relatively uniform fordifferent wavelengths of the incident light by compensating for one ormore of sin α, n2 and sin θ, as described above.

FIG. 14 illustrates a simulation 1400 of diffraction efficiency versusangle of incidence α for an exemplary diffraction grating in accordancewith various embodiments of the diffraction grating 1300 described abovewith reference to with reference to FIGS. 13A and 13B. In particular,the simulation 1400 displays the diffraction efficiency (η) of T−1 orderdiffracted TE polarized green light (λ=520 nm) simulated for adiffraction grating having one or more first lines and second linesformed of polycrystalline silicon on a substrate having n₂=1.77,Λ_(a)=382 nm, h_(nano1)=h_(nano2)=107 nm, W_(nano1)=W_(nano2)=30 nm,p_(nano1)=96 nm and s₁=66 nm, under transmission mode. As illustrated,the range of angle of incidence (Δα), or field of view (FOV), isrelatively wide and exceeds about 40 degrees, outside of which thediffraction efficiency η falls off by about 10% from an efficiency ofabout 32% at α=0.

FIGS. 15A and 15B illustrate 2-dimensional simulations 1500 and 1504 ofphase wavefronts for TE polarized, 520 nm wavelength light beingtransmitted through the diffraction grating 1300 described above withreference to FIGS. 13A and 13B, which corresponds to the simulation 1400illustrated above with reference to FIG. 14. In particular, thesimulations 1500 and 1504 correspond to illumination conditions in whichthe angle of incidence α is 0 degrees and 20 degrees, respectively.

As described more in detail infra, fabrication of diffraction gratingsdisclosed herein may involve patterning processes that includephotolithography and etch. A photolithography process may includedepositing a masking layer, such as a photoresist and/or a hard mask(which may serve as an antireflective coating), on or over a layer ofhigh refractive index material from which the one or more first lines1312 and the second lines 1316 are formed. Subsequently, the mask layermay be developed and/or patterned first into a pattern of masking layer,which serves as a template for patterning the underlying layer of highrefractive index material. Subsequently, using the patterned maskinglayer as a template, the underlying layer of high refractive indexmaterial is patterned into the first and second lines. In variousembodiments, the patterned masking layer is removed, thereby leaving thefirst and second lines. However, under some circumstances, it may bedifficult or undesirable to remove the patterned masking layer from thepatterned first and second lines. For example, removal process for somemasking layers may undesirably damage the surfaces of first and secondlines and/or the surfaces of the exposed substrate. Accordingly,inventors have found that, under some circumstances, the patternedmasking layer may be left-in. In the following, with reference to FIGS.16A-16D, embodiments of a diffracting grating are described, in whichmasking layers are left-in.

FIG. 16A illustrates a cross-sectional side view of a diffractiongrating 1600 comprising a metasurface having geometric phase opticalelements, according to some embodiments, in which the masking layers areleft-in after forming the one or more first lines and the second linesby, e.g., photolithography and etching. In particular, it has been foundthat leaving-in a masking layer having a relatively low refractive indexmay advantageously have little or no impact on the resulting opticalresponse, including diffraction efficiency versus angle of incidence (ηvs α) behavior. Similar to the diffraction grating 1300 illustratedabove with reference to FIGS. 13A and 13B, the diffraction grating 1600includes a substrate 1304 having a surface 1304S, on which a metasurface1608 configured to diffract light having a wavelength in the visiblespectrum is formed. The metasurface 1608 includes one or more firstlines 1312 extending in a first lateral direction (e.g., they-direction) and a plurality of second lines 1316 extending in a seconddirection (e.g., the x-direction). The arrangement of the metasurface1608 may be substantially similar to the arrangement of the metasurface1308 illustrated above with reference to FIGS. 13A and 13B, except, inthe metasurface 1608 of FIG. 16A, on the one or more first lines 1312and on the second lines 1316 are masking layers 1604 that had beenpatterned as a template for etching to form the one or more first lines1312 and the second lines 1316. According to some embodiments, themasking layers 1604 may be photoresist or hard mask layers having arelatively low refractive index, which is lower than the refractiveindex of the material of the one or more first lines 1312 and the secondlines 1316. According to some embodiments, the masking layer 1604, whichmay be a hard mask and/or an anti-reflective layer (ARC), has arefractive index whose value is lower than about 2.0, lower than about1.8, lower than about 1.6 or lower than about 1.4, or whose value iswithin a range defined by any of these values. According to someembodiments, the masking layer 1604 may be formed of asilicon-containing or a silica-containing masking layer.

FIG. 16B illustrates simulations 1610 of diffraction efficiency (η)versus the thickness of the masking layer 1604 (FIG. 16A) for anexemplary diffraction grating similar to the diffraction gratingillustrated above with reference to FIGS. 13A and 13B, except, for thesimulated diffraction grating, a masking layer 1604 is disposed on theone or more first lines 1312 and on the second lines 1316 (FIGS. 13A and13B). In particular, the simulation 1610 displays the diffractionefficiency (η) for TE polarized green light (λ=520 nm) simulated for adiffraction grating having one or more first lines and second linesformed of silicon on a substrate having n₂=1.77 and having formedthereon a masking layer formed of SiO₂ ranging from 0 to 90 nm inthickness, where Λa=382 nm, h_(nano1)=h_(nano2)=107 nm,W_(nano1)=W_(nano2)=30 nm, p_(nano1)=96 nm and s₁=66 nm, undertransmission mode. The simulations 1610 illustrate the simulateddiffraction efficiency curves 1614 and 1618 corresponding to transmitteddiffraction orders T1 and T−1 at α=0, respectively. The simulations 1610illustrates that the presence of the masking layer having a thickness upto 90 nm has almost negligible effect (˜1% or less) on the diffractionefficiency. For example, η ranges by less than about 1% at α=0 for themasking layer having a thickness up to 90 nm.

FIG. 16C illustrates simulations 1620 of diffraction efficiency (η)versus angle of incidence α for an exemplary diffraction gratingsimulated with reference to FIG. 16A, except, for the simulateddiffraction grating, a masking layer 1604 having a fixed thickness of 20nm is disposed on the one or more first lines 1312 and on the secondlines 1316 (FIGS. 13A and 13B). The simulations 1620 illustrate thesimulated diffraction efficiency curves 1614 and 1618 corresponding totransmitted diffraction orders T1 and T−1, respectively. Compared to thesimulation 1400 described above with reference to FIG. 14 for the T−1diffraction order, the simulated diffraction efficiency 1628 illustratesthat the presence of the 20 nm-thick masking layer has almost negligibleeffect (˜1% or less) on the diffraction efficiency or on the field ofview. For example, η is about 32% at α=0, which falls off by about 10%from at +α=21 degrees.

FIG. 16D illustrates simulations 1630 of diffraction efficiency (η)versus angle of incidence α for an exemplary diffraction gratingsimulated with reference to FIG. 16A, except, for the simulateddiffraction grating, a masking layer 1604 having a fixed thickness of 40nm is disposed on the one or more first lines 1312 and on the secondlines 1316 (FIGS. 13A and 13B). The simulations 1630 illustrates thesimulated diffraction efficiency curves 1624 and 1628 corresponding totransmitted diffraction orders T1 and T−1, respectively. Compared to thesimulation 1400 described above with reference to FIG. 14 for T−1diffraction order, the simulated diffraction efficiency 1628 illustratesthat the presence of the 20 nm-thick masking layer has almost negligibleeffect (˜1% or less) on the diffraction efficiency or on the field ofview. For example, η is about 32% at α=0, which falls off by about 10%from at +α=21 degrees.

In the following, with reference to FIGS. 17A-20, simulations ofdiffraction efficiency (η) versus angle of incidence α for exemplarydiffraction gratings formed of different high refractive index materialsare illustrated, where the diffraction gratings are configured todiffract a green light (e.g., λ=520 nm) in the visible spectrum.

FIGS. 17A and 17B illustrate simulations 1700, 1704 of diffractionefficiency (η) versus angle of incidence (α) for an exemplarydiffraction grating formed of amorphous silicon and configured todiffract green visible light. In particular, the simulations 1700 and1704 display the diffraction efficiency (η) of T−1 order diffracted TEand TM polarized green light at λ=520 nm, respectively, incident on thediffraction grating at the α relative to a surface normal. Thesimulations 1700 and 1704 were performed for a diffraction gratinghaving one or more first lines and second lines formed of amorphoussilicon on a substrate having n₂=1.77, where Λa=382 nm,h_(nano1)=h_(nano2)=90 nm, W_(nano1)=W_(nano2)=30 nm, p_(nano1)=96 nmand s₁=66 nm, under transmission mode. The complex refractive index ofrefraction used for the simulations was n=5.02+0.363i. As illustrated,for the TE polarized green light, the range of angle of incidence (Δα),or field of view (FOV), is relatively wide at about 50 (<−30 to >+20)degrees, outside of which the diffraction efficiency η falls off byabout 10% from an efficiency of about 28% at α=0.

FIG. 18 illustrates a simulation 1400 of diffraction efficiency (η)versus angle of incidence (α) for an exemplary diffraction gratingformed of polycrystalline silicon and configured to diffract greenvisible light at λ=520 nm, according to some embodiments. The simulation1400 is the same simulation as that illustrated in FIG. 14, butreplotted with different range of x-axis for easy comparison againstFIGS. 17A, 19 and 20. The complex refractive index of refraction usedfor the simulations was n=4.41+0.182i. As illustrated, the range ofangle of incidence (Δα), or field of view (FOV), is relatively wide andexceeds about 40 degrees, outside of which the diffraction efficiency ηfalls off by about 10% from an efficiency of about 32% at α=0.

FIG. 19 illustrates a simulation 1900 of diffraction efficiency (η)versus angle of incidence (α) for an exemplary diffraction gratingformed of silicon carbide (SiC) and configured to diffract green light,according to some embodiments. In particular, the simulation 1900displays the diffraction efficiency (η) of T−1 order diffracted TEpolarized green light at λ=520 nm incident on the diffraction grating atthe α relative to a surface normal. The simulation 1900 was performedfor a diffraction grating having one or more first lines and secondlines formed of silicon carbide (SiC) on a substrate having n₂=1.77,where Λ_(a)=382 nm, h_(nano1)=h_(nano2)=260 nm, W_(nano1)=W_(nano2)=65nm, p_(nano1)=96 nm and s₁=31 nm, under transmission mode. The complexrefractive index of refraction used for the simulations wasn=2.65+0.005i. As illustrated, for the TE polarized green light, therange of angle of incidence (Δα), or field of view (FOV), is relativelywide at about 40 (˜−20 to ˜+20) degrees, outside of which thediffraction efficiency η falls off by about 10% from an efficiency ofabout 27% at α=0.

FIG. 20 illustrates a simulation 2000 of diffraction efficiency (η)versus angle of incidence (α) for an exemplary diffraction gratingformed of silicon nitride (e.g., Si₃N₄) and configured to diffract greenlight, according to some embodiments. In particular, the simulation 2000displays the diffraction efficiency (η) of T−1 order diffracted TEpolarized green light at λ=520 nm incident on the diffraction grating atthe α relative to a surface normal. The simulation 2000 was performedfor a diffraction grating having one or more first lines and secondlines formed of silicon nitride (e.g., Si₃N₄) on a substrate havingn₂=1.77, where Λa=382 nm, h_(nano1)=h_(nano2)=300 nm,W_(nano1)=W_(nano2)=60 nm, p_(nano1)=96 nm and s₁=36 nm, undertransmission mode. The complex refractive index of refraction used forthe simulations was n=2.20+0.002i. As illustrated, for the TE polarizedgreen light, the range of angle of incidence (Δα), or field of view(FOV), is relatively wide at >40 (˜<−30 to ˜+10) degrees, outside ofwhich the diffraction efficiency η falls off by about 10% from anefficiency of about 21% at α=0.

In the following, with reference to FIGS. 21-24, simulations ofdiffraction efficiency (η) versus angle of incidence (α) for exemplarydiffraction gratings formed of different high refractive index materialsare illustrated, where the diffraction gratings are configured todiffract a blue light (e.g., λ=455 nm) in the visible spectrum.

FIG. 21 illustrates a simulation 2200 of diffraction efficiency (η)versus angle of incidence (α) for an exemplary diffraction gratingformed of polycrystalline silicon and configured to diffract blue light,according to some embodiments. In particular, the simulation 2100displays the diffraction efficiency (η) of T−1 order diffracted TEpolarized blue light at λ=455 nm incident on the diffraction grating atthe α relative to a surface normal. The simulation 2100 was performedfor a diffraction grating having one or more first lines and secondlines formed of polycrystalline silicon on a substrate having n₂=1.77,where Λa=334 nm, h_(nano1)=h_(nano2)=75 nm, W_(nano1)=W_(nano2)=30 nm,p_(nano1)=96 nm and s₁=66 nm, under transmission mode. The complexrefractive index of refraction used for the simulations wasn=4.67+0.636i. As illustrated, for the TE polarized green light, therange of angle of incidence (Δα), or field of view (FOV), is relativelywide at >40 (˜<−30 to ˜>+10) degrees, outside of which the diffractionefficiency η falls off by about 10% from an efficiency of about 22% atα=0.

FIG. 22 illustrates a simulation 2200 of diffraction efficiency (η)versus angle of incidence (α) for an exemplary diffraction gratingformed of amorphous silicon and configured to diffract blue light,according to some embodiments. In particular, the simulation 2200displays the diffraction efficiency (η) of T−1 order diffracted TEpolarized blue light at λ=455 nm incident on the diffraction grating atthe α relative to a surface normal. The simulation 2200 was performedfor a diffraction grating having one or more first lines and secondlines formed of amorphous silicon on a substrate having n₂=1.77, whereΛa=334 nm, h_(nano1)=h_(nano2)=60 nm, W_(nano1)=W_(nano2)=30 nm,p_(nano1)=96 nm and s₁=66 nm, under transmission mode. The complexrefractive index of refraction used for the simulations wasn=5.363+1.015i. As illustrated, for the TE polarized green light, therange of angle of incidence (Δα), or field of view (FOV), is relativelywide at >40 (˜<−30 to ˜+10) degrees, outside of which the diffractionefficiency η falls off by about 10% from an efficiency of about 18% atα=0.

FIG. 23 illustrates a simulation 2300 of diffraction efficiency (η)versus angle of incidence (α) for an exemplary diffraction gratingformed of silicon carbide and configured to diffract blue light,according to some embodiments. In particular, the simulation 2300displays the diffraction efficiency (η) of T−1 order diffracted TEpolarized blue light at λ=455 nm incident on the diffraction grating atthe α relative to a surface normal. The simulation 2300 was performedfor a diffraction grating having one or more first lines and secondlines formed of silicon carbide on a substrate having n₂=1.77, whereΛa=334 nm, h_(nano1)=h_(nano2)=220 nm, W_(nano1)=W_(nano2)=60 nm,p_(nano1)=96 nm and s₁=36 nm, under transmission mode. The complexrefractive index of refraction used for the simulations wasn=2.67+0.01i. As illustrated, for the TE polarized green light, therange of angle of incidence (Δα), or field of view (FOV), is relativelywide at about 40 (˜−18 to ˜+18) degrees, outside of which thediffraction efficiency η falls off by about 10% from an efficiency ofabout 30% at α=0.

FIG. 24 illustrates a simulation 2400 of diffraction efficiency (η)versus angle of incidence (α) for an exemplary diffraction gratingformed of silicon nitride and configured to diffract blue light,according to some embodiments. In particular, the simulation 2400displays the diffraction efficiency (η) of T−1 order diffracted TEpolarized blue light at λ=455 nm incident on the diffraction grating atthe α relative to a surface normal. The simulation 2400 was performedfor a diffraction grating having one or more first lines and secondlines formed of silicon nitride on a substrate having n₂=1.77, whereΛa=334 nm, h_(nano1)=h_(nano2)=260 nm, W_(nano1)=W_(nano2)=60 nm,p_(nano1)=96 nm and s₁=36 nm, under transmission mode. The complexrefractive index of refraction used for the simulations wasn=2.24+0.007i. As illustrated, for the TE polarized green light, therange of angle of incidence (Δα), or field of view (FOV), is relativelywide at about 20 (˜−8 to ˜+12) degrees, outside of which the diffractionefficiency η falls off by about 10% from an efficiency of about 21% atα=0.

FIG. 25 illustrate a top-down view of a diffraction grating 2500comprising a metasurface having geometric phase optical elements,according to some other embodiments. It will be appreciated that someembodiments of metasurfaces disclosed herein may be formed of two tofour sets of nanobeams, each extending in a different direction. FIGS.13A-13B illustrate metasurfaces having two sets of nanobeams, and FIG.25 illustrates metasurface having four sets of nanobeams. In particular,the diffraction grating 2500 of FIG. 25 comprises a 4-level geometricphase metasurface. Similar to the diffraction grating 1300 describedabove with reference to FIGS. 13A and 13B, the diffraction grating 2500includes a substrate, e.g., a waveguide, on which a metasurfaceconfigured to diffract light having a wavelength in the visible spectrumis formed. The metasurface includes one or more first lines 2512extending in a first lateral direction (e.g., the y-direction) and aplurality of second lines 2516 extending in a second direction (e.g.,the x-direction). The one or more first lines 2512 and the second lines2516 are disposed adjacent to one another in the second direction, wherethe first lines 2512 and the second lines 2516 alternatingly repeat inthe second direction at a period less than a wavelength in the visiblespectrum which the metasurface is configured to diffract. In someembodiments, the second lines 2516 are laterally stacked in they-direction between adjacent pairs of first lines 2512. Various featuresof the one or more first lines 1312 and the second lines 1316 of thediffraction grating 2500 are similar to corresponding features of thediffraction grating 1300 described above with reference to FIGS. 13A and13B, except for the following differences.

Unlike the diffraction grating 1300 described above with reference toFIGS. 13A and 13B, the diffraction grating 2500 further comprises one orboth of a plurality of third lines 2514 each extending in a thirddirection and a plurality of fourth lines 2518 each extending in afourth direction. Each of the first, second, third, and fourthdirections may be different from one another. The plurality of thirdlines 2514 may be considered to form a third set of nanobeams and theplurality of fourth lines 2518 may be considered to form a fourth set ofnanobeams. The third lines 2514 are disposed on a first side of thesecond lines 2516 and are interposed in the second direction (e.g.,x-axis direction) between one or more first lines 2512 and the secondlines 2516. The fourth lines 2518 are disposed on a second side of thesecond lines 2516 opposite to the first side and are interposed in thesecond direction (e.g., x-direction) between another one or more firstlines 2512 and the second lines 2516.

Unlike the diffraction grating 1300 described above with reference toFIGS. 13A and 13B, the diffraction grating 2500 may have only one firstline 2512. In some other embodiments, the diffraction grating 2500 mayhave a plurality of first lines 2512, e.g., a pair of first lines suchas the diffraction grating 1300 described above with reference to FIGS.13A and 13B.

In some embodiments, the third lines 2514 have the same length and/orthe fourth lines 2518 have the same length, such that the third lines2514 and/or the fourth lines 2518 coterminate in the third and fourthdirections, respectively. However, other embodiments are possible, inwhich different ones of the third lines 2514 and/or different ones ofthe fourth lines 2518 do not coterminate. In addition, in someembodiments, coterminating third lines 2514 and coterminating fourthlines 2518 have the same length. However, in other embodiments,coterminating third lines 2514 and coterminating fourth lines 2518 havedifferent lengths.

In some embodiments, adjacent ones of the third lines 2514 are separatedby a constant spacing in the first direction (e.g., y-direction), and/oradjacent ones of the fourth lines 2518 are separated by a constantspacing in the first direction. However, other embodiments are possible,in which third lines 2514 and/or the fourth lines 2518 are not separatedby constant spacings. In addition, in some embodiments,constantly-spaced third lines 2514 and constantly-spaced fourth lines2518 have the same constant spacing. However, in other embodiments,constantly-spaced third lines 2514 and constantly-spaced fourth lines2518 have different spacings.

In some embodiments, the third lines 2514 have the same width and/or thefourth lines 2518 have the same width. However, in other embodiments,the third lines 2514 and/or the fourth lines 2518 have different widths.In addition, in some embodiments, widths of the third lines 2514 havingthe same width and the fourth lines 2518 having the same width are thesame. However, in some other embodiments, widths of the third lines 2514having the same width and the fourth lines 2518 having the same widthare different. In addition, in some embodiments, the third lines 2514and the fourth lines 2518 have the same width as one or both of firstlines 2512 and second lines 2416.

In some embodiments, the third lines 2514 extend in the third directionthat is rotated in a counterclockwise direction relative to the one ormore first lines 2512 by an angle smaller than the smallest angle ofrotation of the second lines 2516 relative to the one or more firstlines 2512 when viewed a direction of propagation of an incident light(e.g., into the page). In some embodiments, the second lines 2516 arerotated by 90° or π/2 relative to the one or more first lines 2512, andthe third lines 2514 are rotated by 45° or π/4 relative to the one ormore first lines 2512. In addition, the fourth lines 2518 extend in thefourth direction that is rotated in the counterclockwise directionrelative to the one or more first lines 2512 by an angle greater thanthe smallest angle of rotation of the second lines 2516 relative to theone or more first lines 2512 when viewed the direction of propagation ofan incident light. In some embodiments, the second lines 2516 arerotated by 90° or π/2 relative to the one or more first lines 2512, andthe third lines 2514 are rotated by 135° or 3π/4 relative to the one ormore first lines 2512.

In some embodiments, similar to the combination of wave platesillustrated above with reference to FIG. 12A-12H, the phase differencescaused by the relative orientations of one or more first lines 2512, thesecond lines 2516, the third lines 2514 and the fourth lines 2518, mayvary between 0 and π. When the third lines 2514, the fourth lines 2518and the second lines 2516 and are rotated relative to the one or morefirst lines 2512 by π/4, 3π/4 and π, phase pickups/retardations of π/2,3π/2 and 2π may be achieved, respectively, such that the phasepickups/retardations covering the full 0-2π range may be achieved,according to some embodiments. As a result, by having the fast-axesorientation vary between 0 and π, phase pickups/retardations that coversthe full 0-2π range may be achieved, but with a much more compact unitcell pitch and higher diffraction angles compared to the illustratedexample in FIGS. 12A-12H.

Display Devices Based on Geometric Phase Metasurfaces

In various embodiments of a display system (e.g., with reference back toFIGS. 9A and 9B) a set 1200 of waveguides may include metasurfacediffraction gratings that are configured to operate in transmissionmode. In various embodiments, the set 1200 of waveguides includeswaveguides 670, 680, 690 corresponding to each component color (R, G,B), which in turn has formed therein or thereon respective ones ofincoupling optical elements 700, 710, 720, which may include orcorrespond to the diffraction gratings 1300, 2500 described above withreference to FIGS. 13A and 13B and 25. The waveguides 670, 680, 690additionally has formed therein or thereon respective ones of lightdistributing elements (e.g., OPE's) 730, 740, 750 and/or outcouplingoptical elements (e.g., EPE's) 800, 810, 820, which include orcorrespond to EPE/OPE 1346 described above with reference to FIGS. 13Aand 13B. In operation, in some embodiments, when an incident light beam1330, e.g., visible light, is incident on the metasurface 1308 at anangle of incidence α, the grating 1300, 2500 diffracts the incidentlight into a diffracted light beam 1342, 1338 at a diffraction angle θ₂.When one or both of the diffracted light beams 1338 and 1342 arediffracted at diffraction angles that exceed a critical angle θ_(TIR)for occurrence of total internal reflection for the substrate 1304configured as a waveguide having an index of refraction n₂, i.e., whenone or both of conditions θ₂>θ_(TIR) and θ₁>θ_(TIR) are satisfied, theone or both of the diffracted light beams 1338 and 1342 propagate intheir respective opposite directions along the x-axis by total internalreflection (TIR). Subsequently, in some embodiments, the diffractedlight beam 1346 coupled into the substrate 1304 under TIR mode until itreaches an orthogonal pupil expanders (OPE) 1346 or an exit pupilexpander (EPE) 1346, described above with reference to FIGS. 9A and 9B.

While the gratings 1300, 2500 illustrated above with reference to FIGS.13A and 13B and FIG. 25 are configured to operate in transmissive mode,other embodiments are possible. In some other embodiments, withreference back to FIGS. 9A and 9B, some display devices include a set1200 of waveguides having diffraction gratings that are configured tooperate in reflective mode. In these embodiments, the set 1200 ofwaveguides includes waveguides 670, 680, 690 corresponding to eachcomponent color (R, G, B), which in turn has formed therein or thereonrespective ones of incoupling optical elements 700, 710, 720, whichinclude or correspond to the diffraction grating 2600, whosecross-sectional view is described respect to FIG. 26. The diffractiongrating 2600 includes a metasurface 2608 configured to diffract light ina reflective mode, where, unlike the diffraction gratings 1300, 2500described above with reference to FIGS. 13A and 13B and 25, inoperation, light incident on a side of the metasurface 2608 diffractstowards the same side of the metasurface 2608 as the light-incidentside. The diffraction grating 2600 includes a substrate 1304 having asurface 1304S, on which a metasurface 1308 configured to diffract lighthaving a wavelength in the visible spectrum is formed. The metasurface2608 includes one or more first lines 1312 and a plurality of secondlines 1316 whose material compositions, dimensions and lateralarrangements on the surface 1304S are similar to those of diffractiongratings 1300, 2500 described above with reference to FIGS. 13A and 13Band 25, respectively. In particular, while a top-down view is notillustrated, the metasurface 1308 includes one or more first lines 1312extending in a first lateral direction (e.g., the y-direction) and aplurality of second lines 1316 extending in a second direction (e.g.,the x-direction), where the one or more first lines 1312 and the secondlines 1316 are disposed adjacent to one another in the second directionand alternatingly repeat in the second direction at a period less than awavelength in the visible spectrum.

Without being limited by theory, in some embodiments, similar to themetasurface 1308 described above with reference to FIGS. 13A and 13B, inthe metasurface 2608 of the grating 2600, the one or more first lines1312 and the second lines 1316 are oriented at an angle relative to eachother to cause a phase difference between the visible light diffractedby the one or more first lines 1312 and the visible light diffracted bythe second lines 1316, where the phase difference between the visiblelight diffracted by the one or more first lines 1312 and the visiblelight diffracted by the second lines 1316 is twice the angle.

While not illustrated, similar to the diffraction grating 2500 describedabove with reference to FIG. 25, in some other embodiments, thediffraction grating 2600 further comprises one or both of a plurality ofthird lines 2514 each extending in a third direction and a plurality offourth lines 2518 each extending in a fourth direction. In addition, insome embodiments, the illustrated diffraction grating 2600 has only onefirst line 2512.

Other various possible arrangements of the one or more first lines 1312,the second lines 1316, the third lines 2514 and the fourth lines 2518described above with reference to FIGS. 13A and 13B and 25 may beimplemented in the diffraction grating 2600 of FIG. 26, whose detaileddescription is be omitted.

Unlike the gratings 1300 and 2500 described above with reference toFIGS. 13A and 13B and 25, in the grating 2600, an optically transmissivespacer layer 2604 may be formed over or on, e.g., directly on, the oneor more first lines 1312 and the second lines 1316. In addition, areflective layer 2612 may be formed over or on, e.g., directly on, theone or more first lines 1312 and the second lines 1316, and/or over oron, e.g., directly on, the spacer layer 2604.

In some embodiments, the spacer layer 2604 is formed directly on andcontacting the one or more first lines 1312 and the second lines 1316,such that the one or more first lines 1312 and the second lines 1316 areembedded in the spacer layer 2604. The spacer layer 2604 has a height orthickness h_(spacer) which is greater than the height of the one or morefirst lines 1312 and the second lines 1326 by a height d. The height dmay be within the range of 5 nm to 1 μm, 5 nm to 500 nm or 10 nm to 300nm, according to some embodiments. In some embodiments, the spacer layer2604 has a refractive index n_(spacer) that is lower than the refractiveindices n_(1, bulk) of the bulk material from which the one or morefirst lines 1312 and the second lines 1316 are formed. In someembodiments, the n_(spacer) is also lower than the refractive index n₂of the substrate 1304. In various embodiments, the n_(spacer) has arefractive index of 1 to 2, 1.1 to 1.7, or 1.1 to 1.5, for instance 1.2.In various embodiments, the spacer layer 2604 may be formed of materialthat may be deposited by spin-coating, including poly(methylmethacrylate) (PMMA), spin-on glass, e-beam resist or photo-resist, andpolymer. It will be appreciated that, when deposited by spin-coating,because the as-spin-coated material may undergo a viscous flow, thethickness of the spacer layer 2604 over the one or more first lines 1312and the second lines 1316 may be thinner compared to the thickness ofthe spacer layer 2604 in regions where the one or more first lines 1312and the second lines 1316 are not present, e.g., regions where thespacer layer 2604 is formed directly on the substrate 1304.

In some embodiments, the reflective layer 2612 is formed directly on thespacer layer 2604. In this embodiment, the reflective layer 2612 isseparated from the one or more first lines 2612 and the second lines2616 by the spacer layer 2604 formed thereover. However, in some otherembodiments, the reflective layer 2612 may be formed directly on the oneor more first lines 1312 and the second lines 1316. In theseembodiments, the one or more first lines 1312 and the second lines 1316may be embedded in the reflective layer 2612; i.e., the reflective layer2612 may fill the spaces between the one or more first lines 1312 and/orbetween the second lines 1316.

The reflective layer 2612 may be formed of a material whichsubstantially reflects light, e.g., visible light, such as a metal ormetallic material, such as aluminum, silver, gold, and copper. In someother embodiments, the reflective layer 2612 may be formed of otherlight-reflective material, such as reflective polymer. When formeddirectly on the space layer 2604, the height or thickness h_(r) of thereflective layer 2612 may be sufficiently thick to be substantiallynon-transmissive and free of pores, e.g., thicker than 150 nm, thickerthan 500 nm or thicker than 1 μm, or in a range between thesethicknesses. In embodiments where the reflective layer 2612 is formeddirectly on the one or more first lines 1312 and the second lines 1316,the thickness of reflective layer 2612 may be sufficient to bury the onemore first lines 1312 and the second lines, and may be greater than therespective thickness h_(nano1) and h_(nano2).

FIG. 27 illustrates a simulation 2700 of diffraction (η) versus angle ofincidence (α) for an exemplary diffraction grating in accordance withvarious the embodiments of the diffraction grating 2600 described abovewith reference to FIG. 26. In particular, the simulation 2700 displaysthe diffraction efficiency (η) of T−1 order diffracted TE polarizedgreen light (λ=520 nm) simulated for a diffraction grating having one ormore first lines and second lines formed of polycrystalline silicon on asubstrate having n₂=1.77. Λa=382 nm, h_(nano1)=h_(nano2)=50 nm,W_(nano1)=W_(nano2)=30 nm, p_(nano1)=95.5 nm s₁=65.5 nm and d=50 nm,under reflective mode. As illustrated, the range of angle of incidence(Δα), or field of view (FOV), is relatively wide and exceeds about 45degrees (−25 to +20 degrees), outside of which the diffractionefficiency η falls off by about 10% from an efficiency of about 40% atα=0.

Methods of Fabricating Geometric Phase Metasurfaces

In the following, methods of fabricating geometric phase metasurfacesare described. In some embodiments, the geometric phase metasurfaces maybe fabricated using deposition of a high index material for forming theone or more first lines 1312 and the second lines 1316 on a lower indexsubstrate 1304, followed by patterning using lithography and etchprocesses. In some other embodiments, the geometric phase metasurfacesmay be fabricated using deposition of a high index material of the oneor more first lines 1312 and the second lines 1316 on a lower indexsubstrate 1304, followed by patterning using a nanoimprint technique.

FIGS. 28A-28D illustrate cross-sectional views of intermediatestructures 2800A-2800D, respectively, at various stages of fabricationof a diffraction grating having a geometric phase metasurface usinglithography and etch, according to some embodiments. Referring to theintermediate structure 2800A of FIG. 28A, the method includes providinga substrate 1304 having a surface 1304S suitable for forming ametasurface 1308 thereon. The substrate 1304 includes an opticallytransmissive material having a refractive index n₂ and various othermaterial attributes described above with reference to FIGS. 13A and 13B.The method additionally includes forming on the surface 1304S a highindex layer 1310 having an index of refraction n_(1 bulk) and variousother material attributes described above with reference to FIGS. 13Aand 13B. The high index layer 1310 is suitable, when patterned, forforming the one or more first lines 1312 and second lines 1316 asdescribed above with reference to FIGS. 13A and 13B. The high indexlayer 1310 may be deposited using any suitable technique, such aschemical vapor deposition (CVD), including plasma-based CVD processes,such as plasma-enhanced chemical vapor deposition (PECVD) andthermal-based CVD processes, such as low pressure chemical vapordeposition (LPCVD), according to some embodiments. The high index layer1310 may also be deposited using physical vapor deposition (PVD),evaporation, and atomic layer deposition, among other techniques. Themethod additionally includes forming on the high index layer 1310 amasking layer 1604A. The masking layer 1604A may be formed of or includeone or more layers of materials that are suitable for providing atemplate for subsequent etching of the underlying high index layer 1310.In some embodiments, the masking layer 1604A may be a photoresist, whichmay be spin-coated, followed by a post-bake. In some other embodiments,the masking layer 1604 may include a plurality of layers, including ahard mask layer formed on the high index layer 1310 and a photoresistlayer formed on the hard mask layer. The hard mask layer may beincluded, for example, when a photoresist layer may not providesufficient etch selectivity during the subsequent etch pattern transferto the underlying high index layer 1310. The hard mask layer may alsoserve as an antireflective coating to reduce reflection during thesubsequent exposure process. In some embodiments, the hard mask layermay be a spin-coated polymer or a film deposited by any of thedeposition techniques for depositing the high index layer 1310. Whenincluded, the hard mask layer may provide greater etch selectivity thanthe overlying photoresist layer. In some embodiments, the photoresistmay be a positive photoresist or a negative photoresist. A positivephotoresist is a type of photoresist in which the portion of thephotoresist that is exposed to light becomes soluble to the photoresistdeveloper, whereas a negative resist is a type of photoresist in whichthe portion of the photoresist that is exposed to light becomesinsoluble to the photoresist developer.

In some embodiments, the photoresist and/or the hard mask layer may beformed of a material containing silicon or silicon oxide, which may havesufficient etch selectivity against the high index layer 1310, such thatthe photoresist and/or the hard mask layer remains relatively intactthrough the etching of the underlying high-index layer 1310. In theseembodiments, the silicon or silicon oxide-containing photoresist and/orhard mask layer may remain on top of one or more first lines and/or thesecond lines after patterning, as described above with reference to FIG.16A.

Referring to the intermediate structure 2800B of FIG. 28B, afterdeposition and post-deposition bake, the method includes patterning thephotoresist layer of the mask layer 1604 by selectively exposingportions of the photoresist to a pattern of light. The exposure tolight, e.g., coherent UV light, or an electron beam, causes a chemicalchange, e.g., polymeric crosslinking in the photoresist, which allowsexposed portions of the photoresist to be selectively removed by adeveloper solution for a positive photoresist, or allows unexposedportions of the photoresist to be selectively removed by a developersolution for a negative photoresist. Upon selectively removing, theresulting patterned masking photoresist remains on the high index layer1310, thereby serving as a template for the subsequent patterning theunderlying hard mask layer when included by, e.g., etching. Theresulting intermediate structure 2800C shows the patterned masking layer1604, which includes the patterned photoresist and optionally thepatterned hard mask layer when included.

Referring to the intermediate structure 2800C of FIG. 28C, the patternedmasking layer 1604 may be used as a template to etch the underlying highindex layer 1310 into one or more first lines 1312 extending in a firstlateral direction (e.g., the y-direction) and a plurality of secondlines 1316 extending in a second direction (e.g., the x-direction), asdescribed more in detail above with reference to FIGS. 13A and 13B. Invarious embodiments, the high index layer 1310 may be etched, e.g.,anisotropically dry-etched. The etch process employed may have asuitable selectivity against the masking layer 1604 and/or the substrate1304, such that the portions of the high index layer 1310 are removedwithout prematurely removing the masking layer 1604 and/or withoutundesirably damaging the exposes portions of the substrate 1304.

Referring to the intermediate structure 2800D, in some embodiments, themasking layer 1604 on the one or more first lines 1312 and the secondlines 1316 are removed therefrom. The resist portion of the maskinglayer 1604 may be removed by, e.g., using a liquid resist stripper or anoxygen-based plasma in a process referred to as ashing. If desired andwhen included, the underlying hard mask layer may be subsequentlyremoved using a wet or a dry etch process which selectively removes thehard mask without substantially affecting the one or more first lines1312 and the second lines 1316 or the substrate 1304. However, someembodiments, e.g., the embodiment described above with reference to FIG.16A, the mask layer 1604, e.g., the photoresist/hard mask or the hardmask, may be left-in without being removed.

FIGS. 29A-29D illustrate cross-sectional views of intermediatestructures 2900A-2900D, respectively, at various stages of fabricationof a diffraction grating having a geometric phase metasurfacenanoimprint techniques, according to some embodiments. In someembodiments, the method of forming intermediate structures 2900A, 2900Cand 2900D of FIGS. 29A, 29C and 29D, respectively, is similar to themethod of forming intermediate structures 2800A, 2800C and 2800D ofFIGS. 28A, 28C and 28D, respectively. However, the method of forming theintermediate structure 2900B of FIG. 29B is different from the methodforming the intermediate structure 2800B of FIG. 28B, whose differencesare described below.

Referring to the intermediate structure 2900B of FIG. 29B, unlike themethod described above with reference to FIG. 28B, instead of patterninga photoresist layer by selectively exposing and removing portions of thephotoresist using light or an electron beam, in the illustratedembodiment, a nanoimprint template 2904, or a nanoimprint mold, whichhas predefined topological patterns in accordance with formation of theone or more first lines 1312 and the second lines 1316, is brought intocontact with an imprint resist of the masking layer 1604A. In someembodiments, the template 2904 is pressed into an imprint resist brinedof thermoplastic polymer under certain temperature, e.g., above theglass transition temperature of the imprint resist, thereby transferringthe pattern of the template 2904 into the softened imprint resist. Afterbeing cooled down, the template 2904 is separated from the imprintresist and the patterned resist is left on the high index layer 1310. Insome other embodiments, the after being pressed into the imprint resist,the imprint resist is hardened by crosslinking under U V light.

While not illustrated, reflective-mode metasurfaces, e.g., themetasurface 2608 described with reference to FIG. 26, may be formedthrough additional processing of the intermediate structures shown inFIG. 28D or 29D. For example, a spacer layer 2604 or a reflective layermay be deposited in the open volumes between the one or more first lines1312 and the second lines 1316. In some other embodiments, the one ormore first lines 1312 and the second lines 1316 may be formed by etchingtrenches in a blanket spacer layer 2604 or a blanket reflective layerand subsequently filling the trenches with the high index material ofthe one or more first lines 1312 and the second lines 1316.

It will be appreciated that substrates 1304 configured as waveguideshaving formed thereon metasurfaces according to various embodiments maybe used to form display systems, such as the system 250 (FIG. 6)disclosed herein. For example, the metasurfaces may be utilized asincoupling, light distributing and/or outcoupling optical elements asdescried herein. In some embodiments, after fabrication of themetasurface, the waveguide 2000 may be optically coupled to a lightpipe, such as a light pipe for injecting image information into thewaveguide from a spatial light modulator. The light pipe may be anoptical fiber in some embodiments. Examples of light pipes include theimage injection devices 360, 370, 380, 390, 400 (FIG. 6) and scanningoptical fibers. In some embodiments, a plurality of waveguides eachhaving metasurfaces 1308 may be provided, and each of these waveguidesmay be optically coupled to one or more image injection devices.

Geometric Phase Metasurfaces Having Asymmetric Optical Elements

As described supra, applications of the metasurfaces comprising PBOEsinclude their use as diffraction gratings, e.g., blazed gratings, thatare capable of steering a light beam into several diffracted orders. Forexample, as described above with respect to FIGS. 13A and 13B, thediffraction grating 1300 may be configured to achieve maximum gratingefficiency with respect to a plurality of diffraction orders, e.g., +1and −1 diffraction orders. For example, as described supra with respectto FIGS. 13A and 13B, a blazed grating 1300 based on PBOEs may beconfigured to partially transmit an incident light as a transmittedlight beam 1334 and partially diffracts the incident light as adiffracted light beam of +1 order 1342 at a diffraction angle θ₁ and adiffracted light beam of −1 order 1338 at a diffraction angle θ₂, wherethe diffraction angles are measured relative to the same plane formeasuring α, e.g., the y-z plan. When one or both of the diffractedlight beams 1338 and 1342 are diffracted at a diffraction angle thatexceeds a critical angle θ_(TIR) for occurrence of total internalreflection in the substrate 1304 configured as a waveguide, thediffracted light beams 1338 and 1342 propagate in their respectiveopposite directions along the x-axis under total internal reflection(TIR) until the light beams reach the OPE's/EPE's 1346, which maycorrespond to the light distributing elements 1214, 1224, 1234 and theout-coupling optical elements 1250, 1252, 1254 (FIG. 9B). However, forsome applications, it may be desirable to concentrate the diffractedlight into a one of a plurality of diffraction orders, e.g., one of the+1 diffraction order 1338 or the −1 diffraction order 1338, whilereducing the other of the plurality of diffraction orders, e.g., theother of the +1 order 1338 or −1 diffraction order 1338. For example,referring back to FIGS. 13A/13B, when the substrate 1304 is configuredas a waveguide such that the diffracted light beams 1338 and 1342propagate along the x-axis under total internal reflection (TIR) untilthe light beams reach the OPE's/EPE's 1346 disposed at one side,concentrating the diffracted light into a single order of diffractionprovides a greater amount of light that is actually available to beoutputted to the viewer.

With reference to FIGS. 30A and 30B, a 2-phase level, asymmetricgeometric phase metasurface configured to steer light in a particulardiffraction order is illustrated. FIGS. 30A and 30B illustrate across-sectional side view and a top-down view, respectively, of adiffraction grating 3000 that includes a metasurface 3008 configured todiffract visible light having a wavelength, where the metasurfacecomprises a plurality of repeating unit cells 1320 a. Each unit cellcomprises a first set of nanobeams comprising two or more firstnanobeams 3012 that are asymmetric in the sense that at least two of thefirst nanobeams 3012 have different widths compared to one another. Eachunit cell also comprises a second set of nanobeams comprising aplurality of second nanobeams 3016 that include asymmetric secondnanobeams 3016, at least two of which have different widths. The secondnanobeams are disposed adjacent to the first nanobeams and separatedfrom each other by a sub-wavelength spacing, wherein the first nanobeams3012 and the second nanobeams 3016 have different orientations.Advantageously, it has been found that metasurfaces with theseasymmetric nanobeams may diffract light such that the light is moreefficiently steered into one of a plurality of diffraction orders, e.g.,one of the +1 diffraction order 1342 or the −1 diffraction order 1338,while reducing the other of the plurality of diffraction orders, e.g.,the other of the +1 order 1342 or −1 diffraction order 1338.

In some embodiments, the diffraction grating 3000 comprises a 2-levelgeometric phase metasurface. The cross-sectional side view illustratedwith reference to FIG. 30A is that of a cross-section taken along theline AA′ of FIG. 30B. The diffraction grating 3000 includes a substrate1304 having a surface on which is formed a metasurface 3008 configuredto diffract light having a wavelength in the visible spectrum. Themetasurface 3008 includes first lines or nanobeams 3012 having a firstorientation and extending generally in a first lateral direction (e.g.,the y-direction) and a plurality of second lines or nanobeams 3016extending generally in a second direction (e.g., the x-direction). Thefirst lines or nanobeams 3012 may be considered to form a first set ofnanobeams and the second lines or nanobeams 3016 may be considered toform a second set of nanobeams. The first lines 3012 and the secondlines 3016 are disposed adjacent to one another in the second direction,and the first lines 3012 and the second lines 3016 alternatingly repeatin the second direction at a period, e.g., a period less than thewavelength of light for which the metasurface is configured to diffract.Advantageously, in comparison to structures such as those of U.S. Pat.No. 9,507,064, metasurfaces with the space-variant orientations canefficiently diffract light having multiple polarizations, e.g., TE andTM polarizations.

It will be appreciated that the physical and optical properties of thediffraction grating 3000 including, e.g., refractive indices of variousmaterials as well as the operational principles of the grating, aresimilar to various embodiments described above, e.g., the diffractiongrating 1300 described above with respect to FIG. 13A/13B. In addition,the unit cell pitch Λ_(a) of the diffraction grating 3000, as well asdimensions, e.g., height, length and width, of the first nanobeams 3012and of the second nanobeams 3016 are similar to various embodimentsdescribed above, and their detailed description is omitted herein forbrevity.

However, unlike some embodiments described above, at least one of thefirst nanobeams 3012 have a different width than another of the firstnanobeams 3012, and at least one of the second nanobeams 3016 have adifferent width than another of the second nanobeams 3016. In theillustrated embodiment, a unit cell includes the first set of nanobeamscomprising a pair of first nanobeams 3012, having a first widthW_(nano1-1) and a second width W_(nano1-2), that are different from eachother. The unit cell additionally includes the second set of nanobeamscomprising a plurality of second nanobeams 3016, having a third widthW_(nano2-1) and a fourth width W_(nano2-2), that are different from eachother. Thus, in the illustrated embodiment, the first set of nanobeamsincludes alternating nanobeams having two different widths, and thesecond set of nanobeams includes alternating nanobemas having twodifferent widths. However, embodiments are not so limited and the firstand/or second set of nanobeams can have additional nanobeams that haveother widths.

In the following, various configurations including dimensions andgeometric arrangements of the first lines 3012 and the second lines 3016are described, whose combined effect is to steer diffracted light intoone of a plurality of diffraction orders while reducing the other(s) ofthe plurality of diffraction orders, as well as achieving variousdesirable optical properties described above, including one or more of arelatively high diffraction angle, a relatively high diffractionefficiency, a relatively wide range of acceptance angle and a relativelyuniform efficiency within the range of acceptance angle, and relativelyhigh efficiency for both TE and TM polarizations.

In detail, referring to FIG. 30A, in operation, when an incident lightbeam 1330, e.g., visible light, is incident on the metasurface 3008 atan angle of incidence α measured relative to a plane normal to thesurface 1304S and extending in a direction parallel to the first lines1312, e.g., the y-z plane, the grating 3000 partially transmits theincident light as a transmitted light beam and partially diffracts theincident light as a diffracted light beam of +1 order 1342 at adiffraction angle θ₁, while substantially suppressing a diffracted lightbeam of −1 order (not shown for clarity) at a diffraction angle θ₂,where the diffraction angles are measured relative to the same plane formeasuring α, e.g., the y-z plan. Similar to as described above, when thediffracted light beam of +1 order 1342 is diffracted at a diffractionangle that exceeds a critical angle θ_(TIR) for occurrence of totalinternal reflection in the substrate 1304 configured as a waveguide, thediffracted light beams propagate along the x-axis under total internalreflection (TIR) until the light beams reach the OPE's/EPE's 1346 (notshown for clarity, see, e.g., FIG. 13A.13B).

In various embodiments, each of W_(nano1) of the first lines 1312 andW_(nano2) of the second lines 1316 is smaller than the wavelength oflight the metasurface 1308 is configured to diffract, and is preferablysmaller than a wavelength in the visible spectrum. In some embodiments,each of the W_(nano1-1), W_(nano1-2), W_(nano2-1) and W_(nano2-2) is inthe range of 10 nm to 1 μm, 10 nm to 500 nm, 10 nm to 300 nm, 10 nm to100 nm or 10 nm to 50 nm, for instance 30 nm. In some embodiments,W_(nano1-1) is substantially equal to W_(nano2-1) and W_(nano1-2) issubstantially equal to W_(nano2-2). In some other embodiments, each ofthe W_(nano1-1), W_(nano2-1), W_(nano1-2) and W_(nano2-2) may bedifferent.

According to some embodiments, immediately adjacent ones of the firstlines 1312 in the second direction (x-direction) are separated by aspacing s₁₋₁. In addition, one of the first lines 1312 are separatedfrom the one of the second lines 1316 on opposite sides by differentconstant spacing s₁₋₂ and s₁₋₃. According to some embodiments, each ofthe s₁₋₁, s₁₋₂ and s₁₋₃ is smaller than the wavelength the metasurface3008 is configured to diffract.

According to some embodiments, immediately adjacent ones of the secondlines 3016 in the first direction (y-direction) are separated byspacings s₂₋₁ and s₂₋₂ that alternatingly repeat with the alternatinglyrepeating second lines 3016 having two different widths W_(nano2-1) andW_(nano2-2). According to some embodiments, each of the s₂₋₁ and s₂₋₂ issmaller than the wavelength the metasurface 3008 is configured todiffract.

With continued reference to FIG. 30A, the first lines 3012 and thesecond lines 3016 have a height h_(nano) which may be the same ordifferent, and that are similar in dimensions as described above, e.g.,with respect to FIGS. 13A/13B, whose descriptions with respect to thedimensions and the technical effects, e.g., on the field of view (FOV),are not described herein for brevity. Furthermore, the desired ratios ofspacing to height of the different nanobeams may be realized where,e.g., each of the spacings s₁₋₁, s₁₋₂, s₁₋₃, s₂₋₁ and s₂₋₂ is in therange of 10 nm to 1 μm, 10 nm to 300 nm, 10 nm to 100 nm or 10 nm to 50nm, for instance 30 nm. Of course, relatively lower values of s₁₋₁,s₁₋₂, s₁₋₃, s₂₋₁ and s₂₋₂ may be realized where h_(nano1) and h_(nano2)have correspondingly relatively lower values.

According to various embodiments, the combination of s₁₋₁ and one ofW_(nano1-1) or W_(nano1-2) may be selected such that a pitch (p_(nano1))of the first lines 3012, defined as a sum of s₁₋₁ and one of W_(nano1-1)or W_(nano1-2), has a value obtained by a sum of W_(nano1-1),W_(nano1-2) selected from ranges of 10 nm to 1 μm, 10 nm to 500 nm, 10nm to 300 nm, 10 nm to 100 nm or 10 nm to 50 nm, and s₁ selected fromranges of 10 nm to 1 μm, 10 nm to 300 nm, 10 nm to 100 nm or 10 nm to 50nm. For instance p_(nano1)=95.5 nm in some embodiments.

Of course, relatively small values of s₁₋₁, s₁₋₂, s₁₋₃, s₂₋₁ and s₂₋₂may be realized and h_(nano) may have correspondingly relatively smallvalues. Advantageously, using a material with relatively high refractiveindex n₁ to form the first lines 1312 and/or the second lines 1316,relatively small values of s₁₋₁, s₁₋₂, s₁₋₃, s₂₋₁ and s₂₋₂, h_(nano) maybe obtained. This is because, as the inventors have found, the quantityh_(nano) may be inversely proportional to the bulk refractive index ofthe material forming the first lines 3012 and the second lines 3016.Accordingly, for a material having bulk refractive index of 2.0-2.5,2.5-3.0, 3.0-3.5 and higher than 3.5, h_(nano) may be in the range of500 nm to 1 μm, 300 nm to 500 nm, 100 nm to 300 nm and 10 nm to 100 nm,respectively, in various embodiments. Thus, by the particularcombination of a material having a high bulk refractive index n₁ of thefirst lines 3012 and the second lines 3016 and the correspondingdimensions s₁₋₁, s₁₋₂, s₁₋₃, s₂₋₁ and s₁₋₂, h_(nano), the overall pitchΛ_(a) may also be correspondingly decreased, which in turn increases thediffraction angle θ, as described further below.

FIGS. 31A and 31B illustrate simulations 3100, 3104 of diffractionefficiency (η) versus angle of incidence (α) for an exemplarydiffraction grating formed of polycrystalline silicon and configured todiffract green visible light. In particular, the simulations 3100 and3004 display the diffraction efficiencies (η) of T+1 (3114, FIG. 31A)and T−1 (3118, FIG. 31A) order diffracted TE polarized green light atλ=520 nm and of T+1 (3124, FIG. 31B) and T−1 (3128, FIG. 31B) order TMpolarized green light at λ=520 nm, respectively, incident on thediffraction grating at the α relative to a surface normal. Thesimulations 3100 and 3104 were performed for a diffraction gratinghaving first lines and second lines formed of polycrystalline silicon ona substrate having n₂=1.77, where Λ_(a)=382 nm, h_(nano1)=107 nm,W_(nano1-1)=W_(nano2-1)=30 nm and W_(nano1-2)=W_(nano2-2)=45 nm, s₁₋₁=58nm, s₁₋₂=23 nm, s₁₋₃=35 nm, s₂₋₁=s₂₋₂=58 nm, under transmission mode.

As illustrated in FIG. 31A, for TE polarized light, the diffractiongrating 3000 diffracts the incident light relatively efficiently intothe T+1 order diffracted beam 3114, while reducing the T−1 orderdiffracted beam 3118, with corresponding diffraction efficienciesexceeding 50% and about 10%, respectively, at α=0. For the T+1 order TEpolarized green light, the range of angle of incidence (Δα), or field ofview (FOV), is relatively wide at about 50 (˜20 to >+20) degrees,outside of which the diffraction efficiency η falls off by about 10% ormore from an efficiency exceeding 50% at α=0. As illustrated in FIG.31B, for TM polarized light, the diffraction grating 3000 diffracts theincident light relatively evenly between the T+1 order diffracted beam3124 and the T−1 order diffracted beam 3128, with correspondingdiffraction efficiencies lower than 20% at α=0.

FIGS. 32A and 32B illustrate simulated diffraction efficiencies (η)versus angle of incidence (α) for an exemplary diffraction gratingformed of amorphous silicon, for TE and TM polarized green light,respectively, according to some embodiments. In particular, thesimulations 3200 and 3204 display the diffraction efficiencies (η) ofT+1 (3214, FIG. 32A) and T−1 (3218, FIG. 32A) order diffracted TEpolarized green light at λ=520 nm and of T+1 (3224, FIG. 32B) and T−1(3228, FIG. 32B) order TM polarized green light at λ=520 nm,respectively, incident on the diffraction grating at the α relative to asurface normal. The simulations 3200 and 3204 were performed for adiffraction grating having first lines and second lines formed ofamorphous silicon on a substrate having n₂=1.77, where Λ_(a)=382 nm,h_(nano)=85 nm, W_(nano1-1)=W_(nano2-1)=25 nm andW_(nano1-2)=W_(nano2-2)=40 nm, s₁₋₁=63 nm, s₁₋₂=25 nm, s₁₋₃=38 nm,s₂₋₁=s₂₋₂=63 nm, under transmission mode operation.

As illustrated in FIG. 32A, for TE polarized light, the diffractiongrating 3000 diffracts the incident light relatively efficiently intothe T+1 order diffracted beam 3214, while reducing the T−1 orderdiffracted beam 3218, with corresponding diffraction efficiencies ofabout 42% and about 13%, respectively, at α=0. For the T+1 order TEpolarized green light, the range of angle of incidence (Δα), or field ofview (FOV), is relatively wide at >40 (<−30 to >+10) degrees, outside ofwhich the diffraction efficiency η falls off by about 10% or more froman efficiency exceeding 40% at α=0. As illustrated in FIG. 32B, for TMpolarized light, the diffraction grating 3000 diffracts the incidentlight relatively evenly between the T+1 order diffracted beam 3224 andthe T−1 order diffracted beam 3228, with corresponding diffractionefficiencies exceeding 15% at α=0.

FIGS. 33A and 33B illustrate simulated diffraction efficiencies (η)versus angle of incidence (α) for an exemplary diffraction gratingformed of amorphous silicon, for TE and TM polarized green light,respectively, according to some embodiments. In particular, thesimulations 3300 and 3304 display the diffraction efficiencies (η) ofT+1 (3314, FIG. 33A) and T−1 (3318, FIG. 33A) order diffracted TEpolarized green light at λ=520 nm and of T+1 (3324, FIG. 32B) and T−1(3328, FIG. 32B) order TM polarized green light at λ=520 nm,respectively, incident on the diffraction grating at the α relative to asurface normal. The simulations 3300 and 3304 were performed for adiffraction grating having first lines and second lines formed ofamorphous silicon on a substrate having n₂=1.77, where Λ_(a)=382 nm,h_(nano1) 85 nm, W_(nano1-1)=W_(nano2-1)=30 nm andW_(nano1-2)=W_(nano2-2)=45 nm, s₁₋₁=58 nm, s₁₋₂=23 nm, s₁₋₃=35 nm,s₂₋₁=s₂₋₂=58 nm, under transmission mode.

As illustrated in FIG. 33A, for TE polarized light, the diffractiongrating 3000 diffracts the incident light relatively efficiently intothe T+1 order diffracted beam 3314, while reducing the T−1 orderdiffracted beam 3318, with corresponding diffraction efficiencies ofabout 39% and about 13%, respectively, at α=0. For the T+1 order TEpolarized green light, the range of angle of incidence (Δα), or field ofview (FOV), is relatively wide at >40 (<−30 to >+10) degrees, outside ofwhich the diffraction efficiency η falls off by about 10% or more froman efficiency exceeding 35% at α=0. As illustrated in FIG. 33B, for TMpolarized light, the diffraction grating 3000 diffracts the incidentlight relatively evenly between the T+1 order diffracted beam 3324 andthe T−1 order diffracted beam 3328, with corresponding diffractionefficiencies exceeding 15% at α=0.

Various example embodiments of the invention are described herein.Reference is made to these examples in a non-limiting sense. They areprovided to illustrate more broadly applicable aspects of the invention.Various changes may be made to the invention described and equivalentsmay be substituted without departing from the true spirit and scope ofthe invention.

For example, while advantageously utilized with AR displays that provideimages across multiple depth planes, the augmented reality contentdisclosed herein may also be displayed by systems that provide images ona single depth plane, and/or with virtual reality displays. In someembodiments where multiplexed image information (e.g. light of differentcolors) is directed into a waveguide, multiple metasurfaces may beprovided on the waveguide, e.g., one metasurface active for each colorof light. In some embodiments, the pitch or periodicity, and/orgeometric sizes, of the protrusions forming the metasurface may varyacross a metasurface. Such a metasurface may be active in redirectinglight of different wavelengths, depending upon the geometries andpitches at the locations where that light impinges on the metasurfaces.In some other embodiments, the geometries and pitches of metasurfacefeatures are configured to vary such that deflected light rays, even ofsimilar wavelengths, propagate away from the metasurface at differentangles. It will also be appreciated that multiple separated metasurfacesmay be disposed across a substrate surface, with each of themetasurfaces having the same geometries and pitches in some embodiments,or with at least some of the metasurfaces having different geometriesand/or pitches from other metasurfaces in some other embodiments.

Also, while advantageously applied to displays, such as wearabledisplays, the metasurfaces may be applied to various other devices inwhich a compact, low-profile light redirecting element is desired. Forexample, the metal surfaces may be applied to form light redirectingparts of optical plates (e.g., glass plates), optical fibers,microscopes, sensors, watches, cameras, and image projection devicesgenerally.

In addition, many modifications may be made to adapt a particularsituation, material, composition of matter, process, process act(s) orstep(s) to the objective(s), spirit or scope of the present invention.Further, as will be appreciated by those with skill in the art that eachof the individual variations described and illustrated herein hasdiscrete components and features which may be readily separated from orcombined with the features of any of the other several embodimentswithout departing from the scope or spirit of the present inventions.All such modifications are intended to be within the scope of claimsassociated with this disclosure.

The invention includes methods that may be performed using the subjectdevices. The methods may comprise the act of providing such a suitabledevice. Such provision may be performed by the user. In other words, the“providing” act merely requires the user obtain, access, approach,position, set-up, activate, power-up or otherwise act to provide therequisite device in the subject method. Methods recited herein may becarried out in any order of the recited events which is logicallypossible, as well as in the recited order of events.

Example aspects of the invention, together with details regardingmaterial selection and manufacture have been set forth above. As forother details of the present invention, these may be appreciated inconnection with the above-referenced patents and publications as well asgenerally known or appreciated by those with skill in the art. The samemay hold true with respect to method-based aspects of the invention interms of additional acts as commonly or logically employed.

For ease of description, various words indicating the relative positionsof features are used herein. For example, various features may bedescribed as being “on,” “over,” at the “side” of, “higher” or “lower”other features. Other words of relative position may also be used. Allsuch words of relative position assume that the aggregate structure orsystem formed by the features as a whole is in a certain orientation asa point of reference for description purposes, but it will beappreciated that, in use, the structure may be positioned sideways,flipped, or in any number of other orientations.

In addition, though the invention has been described with reference toseveral examples optionally incorporating various features, theinvention is not to be limited to that which is described or indicatedas contemplated with respect to each variation of the invention. Variouschanges may be made to the invention described and equivalents (whetherrecited herein or not included for the sake of some brevity) may besubstituted without departing from the true spirit and scope of theinvention. In addition, where a range of values is provided, it isunderstood that every intervening value, between the upper and lowerlimit of that range and any other stated or intervening value in thatstated range, is encompassed within the invention.

Also, it is contemplated that any optional feature of the inventivevariations described may be set forth and claimed independently, or incombination with any one or more of the features described herein.Reference to a singular item, includes the possibility that there areplural of the same items present. More specifically, as used herein andin claims associated hereto, the singular forms “a,” “an,” “said,” and“the” include plural referents unless the specifically stated otherwise.In other words, use of the articles allow for “at least one” of thesubject item in the description above as well as claims associated withthis disclosure. It is further noted that such claims may be drafted toexclude any optional element. As such, this statement is intended toserve as antecedent basis for use of such exclusive terminology as“solely,” “only” and the like in connection with the recitation of claimelements, or use of a “negative” limitation.

Without the use of such exclusive terminology, the term “comprising” inclaims associated with this disclosure shall allow for the inclusion ofany additional element—irrespective of whether a given number ofelements are enumerated in such claims, or the addition of a featurecould be regarded as transforming the nature of an element set forth insuch claims. Except as specifically defined herein, all technical andscientific terms used herein are to be given as broad a commonlyunderstood meaning as possible while maintaining claim validity.

The breadth of the present invention is not to be limited to theexamples provided and/or the subject specification, but rather only bythe scope of claim language associated with this disclosure. Indeed, thenovel apparatus, methods, and systems described herein may be embodiedin a variety of other forms; furthermore, various omissions,substitutions and changes in the form of the methods and systemsdescribed herein may be made without departing from the spirit of thedisclosure. For example, while blocks are presented in a givenarrangement, alternative embodiments may perform similar functionalitieswith different components and/or circuit topologies, and some blocks maybe deleted, moved, added, subdivided, combined, and/or modified. Each ofthese blocks may be implemented in a variety of different ways. Anysuitable combination of the elements and acts of the various embodimentsdescribed above can be combined to provide further embodiments. Thevarious features and processes described above may be implementedindependently of one another, or may be combined in various ways. Allsuitable combinations and subcombinations of features of this disclosureare intended to fall within the scope of this disclosure.

What is claimed is:
 1. A method of fabricating an optical system,comprising: providing a substrate; forming a metasurface on thesubstrate, the metasurface comprising a plurality of unit cells, each ofthe unit cells comprising first and second sets of nanobeams, whereinforming the unit cells comprises: forming the first set of nanobeamscomprising one or more first nanobeams; and forming the second set ofnanobeams adjacent to the one or more first nanobeams, the second set ofnanobeams comprising a plurality of second nanobeams that are separatedfrom each other by a sub-wavelength spacing, wherein the wavelength is avisible light wavelength, wherein the one or more first nanobeams andthe plurality of second nanobeams are elongated in different orientationdirections, and wherein the unit cells repeat at a period less than orequal to the wavelength.
 2. The method of claim 1, wherein forming theone or more first nanobeams and forming the second nanobeams compriseslithographically defining the first and second nanobeams.
 3. The methodof claim 1, wherein forming the one or more first nanobeams and formingthe second nanobeams comprises forming the first and second nanobeams bynanoimprinting.
 4. The method of claim 1, wherein forming the one ormore first nanobeams and forming the second nanobeams are performedsimultaneously.
 5. The method of claim 1, wherein the one or more firstnanobeams have the same width.
 6. The method of claim 1, wherein thesecond nanobeams of each unit cell have the same width.
 7. The method ofclaim 1, wherein the units cells have a period less than or equal to awavelength of one of blue light, green light or red light.
 8. Theoptical system of claim 1, wherein the one or more first nanobeams andthe second nanobeams comprise a bilayer comprising a lower layer havinga first refractive index and an upper layer having a second refractiveindex lower than the first refractive index.
 9. The method of claim 1,wherein the one or more first nanobeams and the second nanobeams areoriented at an angle relative to each other to cause a phase differencebetween the visible light diffracted by the one or more first nanobeamsand the visible light diffracted by the second nanobeams, wherein thephase difference is twice the angle.
 10. The method of claim 1, whereinthe one or more first nanobeams and the second nanobeams are oriented inorientation directions that are rotated by about 90 degrees relative toeach other.
 11. The method of claim 1, wherein the one or more firstnanobeams and the second nanobeams have a height less than thewavelength.
 12. The method of claim 1, wherein the one or more firstnanobeams and the second nanobeams are formed of a semiconductormaterial.
 13. The optical system of claim 1, wherein the one or morefirst nanobeams and the second nanobeams are configured to diffract thevisible light at a diffraction efficiency greater than 10% at adiffraction angle greater than 50 degrees relative to a surface normalplane.
 14. The method of claim 1, wherein the one or more firstnanobeams and the second nanobeams are formed on a substrate and formedof a material whose bulk refractive index is greater than a refractiveindex of the substrate by at least 0.5.
 15. The method of claim 14,wherein the substrate has a refractive index greater than 1.5.
 16. Themethod of claim 1, further comprising forming a metallic reflectivelayer over the one or more first nanobeams and the second nanobeams. 17.The method of claim 1, further comprising forming a third set ofnanobeams comprising a plurality of third nanobeams elongated in adifferent orientation relative to the first one or more first nanobeamsand the nanobeams of the plurality of second nanobeams, wherein thethird nanobeams are formed interposed between the one or more firstnanobeams and the second nanobeams.
 18. The method of claim 17, furthercomprising forming a fourth set of nanobeams comprising a plurality offourth nanobeams elongated in a different orientation relative to theone or more first nanobeams, the plurality of second nanobeams and theplurality of third nanobeams, wherein the fourth nanobeams are disposedon a side of the second nanobeams in the second orientation directionthat is opposite to a side in which the third nanobeams are disposed.19. The method of claim 18, wherein the fourth nanobeams extend in afourth orientation direction that is rotated in a counterclockwisedirection relative to the one or more first nanobeams by an anglegreater than the smallest angle of rotation in the counterclockwisedirection of the second nanobeams relative to the one or more firstnanobeams when viewed a direction of propagation of an incident light.20. The method of claim 19, wherein the fourth orientation direction andthe third orientation direction are rotated by about 90 degrees relativeto each other.